From fd52ccb6d1bc4d4560556dfb7ab1d0232e793cc1 Mon Sep 17 00:00:00 2001 From: flavis Date: Thu, 26 Nov 2020 17:09:16 +0100 Subject: [PATCH] update ana --- ws2020/ana/uebungen/ana3.pdf | Bin 171661 -> 171745 bytes ws2020/ana/uebungen/ana3.tex | 42 +++++++++++++++++------------------ 2 files changed, 21 insertions(+), 21 deletions(-) diff --git a/ws2020/ana/uebungen/ana3.pdf b/ws2020/ana/uebungen/ana3.pdf index 669c109c0340bdd0ff87e7b0bb98426af593d2a5..748279668146e9f8c2cf4c34a41f43499c2acfce 100644 GIT binary patch delta 19792 zcmV)LK)Jt-y$a#I3XmiMGcc3kSSWw(J=>DoMt1M|3g#hOR9Wop`^C0WCC5%Gt9awA zWbIb0eV}%r8QK(QLvrjyoBVsuX#fNoIJl7*Y2?b2AP(54``oY1-@g3AcVcmUc*Gai z3%>a0M_;{s^xJ1i4@5AQsc%^@oTB^?< zue8?7*GlO(ce}?cvAljPmIr)zvxTSi@rZBgrGk&V=6?CF+3ha>@>h5J>-GNXN&dfo zyxDIK$IW_|zyB?KIoltz-Qz#M{N1B(UOxKIM*?=q7oyx14@?EQ_{+OTKm3_5uHa9< zTX6WuFMf$HzFTMouQ+(zE?$2;`uEd0%YU0II{jL!r!a3)$XRU4)hmbrOgO2wIP!PEpy6u@wC$wG5|cenfL*dslY!4lGN$r>eh zU$DlBTQ6CoQVN0dv{r42>3TE_4I`4K@6dgDy zJljKe@Wzce9r|gpMDxtHKyXBuoF>ukZ0pl>E}vcecqxhQ=m9wS#|Yv<5(ksE{V?WJ53m*eq`n z1{F#Za09Ef@i=HdwkZxySt<=rX-*dvtS?BlFa3$b-@aB(?`du9+=-yn*&Xxh#Gr(l z;7#5X&265z_eYY*wlarNXUXMNhIUUY2q-~lAh^sRJlyZz;^P|Q%Kk2&OD@HyMVR-WV^ z+}`Z63IrSkr3sD)$V#~Eo6U8$JLFK-Z!x5ew*38FZpqR1?ydk<)XH#hFty-hgwkTZ z+Z^*RTxDPp^=^~xGYYW~>>AKu3Fw*wQ0KZ_kw<^7Grc-E7dA7f@pXg8eZnrt;te|m zTd-Q9C#MTf?DP0BpbvLe`k%`7I6sIjU6fD)37aw9ZAJpIBkit zWQG}~`wj)zlP#5=DhkcR4Bm?#@Lnw8y>zaT^T$dCbVCE6(=co7ST^r5DnLK!>e}@e zl+=IQn{6d;N6b+Ly}Y8_SLf>PbO*vKe0CZNX~O01DaP-9&^-nHBHTlBPg#y*GDHBb zmlX;rr$|B!*y|L5>jjP=;S?p(1wMjXtZHw)=3EfeKp_KXqUP0fIZx`rI!^^tzrEdF zAB)E>r$B?cw!NAX@GG_N(<+hc{6|tNrdNNhG=RWiL!U)U&-##vvr^jp($2zef5c;Ftto@gJGM0JC%w zrPVVuHdj}hI6@XBgQmB3)I8?_VWQBzX-79)4IK31(k9ak+ zrcZ?rlfQK^=Sm;?tae79^}H-ii#h7l`a43Wa&YG`aH_pVX;#i0Jk<#ICyHv|;R4Yl zY)!lS%x$2hXj1JG8G6u!O++@8SOtHEYy?ffDtu(3jEfJ3a50Yx924*~SO82z0M!*@ z7T%P0x+@Aaed$ckq;-Ai%p?jVvzbX0-cgW%Bl$pR^K;@fDHB3un16$UCRYm3OfhSxITNJv|Eg+l8@$@$%C0UYbdFk^2jP zCuNuZ#@gZNjPcZL(uY3ic-+T-IKiD#GND2(8ypj%Yr23Fqh4%OkbUldtFEPeG0jm z)1|;X2tg{e=a-`ez0*{hXXE-GDIpEk)S*44b+M_E;$M&ssN!O{erkW1t5QHTPsp>Y zr-{%FR!T17uGYV26!$gay;B%RI*in+RFc)-~##bp!#jEhiM&I>mZkOur#V0UEH zc8bZ3N->E%#bjnnF-^|z4g|*28XyvNgZ-6t^mOHPOp()Z)62Qdl%HDESNbIA5$=;7 zO^rIDALab~kZ8LRBdC9`Y3kD%Ju@z&=RfI;-g%@IBWY{ysiZO@_h&}t{``kkahK-) zAgS@xSikaCcAWne}9%>ttVcg`Ku)P^UU2 zf^7vqsg~#9+{(0=fqFcOOzdU7qr^}dFqY!iq12Pq1>IO5vrN@8!sVj)4}|B69er*n zwIv(v3_%%75(1Z+ruF? zj3X*KCU3lAGab}EM1Gm6tLS_BNP?eex9jYmOp%-F7U6&NKvh0ThJTrBji^5e1TM=4V3R)7%1Nd)jN!opoZn!DKdrdL|2rx1G{Ht zD(4%Oc(%vG-?|M%*#SIgV|HapzyuJezIN%?)YITkC`ryS!4 z-xPnqX+eK@u=yAXKp>irU8oOqeor3R^Rt|5irZ>2@N;r-3kSA_V68O7Y})#C!mC4E zfvWyIkd0WyogJ#oq^a(SCbpxwRK^E!eowL0MS_g zRSRHv@=3kgH3_Z;uUJS1hzMVO@`a#9bfV4XM%RKB*zT3DM7KE z?+TLxPyO?4PBLEkX|Kq9vx6;87%6LOlUgtS%Lg?xd%n)04MFGZu}~*EzM$MC4_`PN z#U6iD$%7qBK3~OBW68>xYLuxF`Bih~gY$bGGhQ?%$7}h=CiSdl9aZZePy>Vrd`FoNxM4me(HXoSwx*>OsoLv;WGxpRZ z+@wWbkp$r~i5uWxe?%V~yzOkC|3B|Dz!QIWwMkgKXi5#Sxu3}9tpLY1C_wff0q-cI zW{GNOZJXRtQYJ-W3jJN4GpD4`IOe3Dn$n(mp8M6%{P1AV{ep`9tyd$H;sLawovVTH z+~fNO`%~SL$z3@TRGYz00$W;_{~_)(vkDchG{7uC9Hn~ zw5ZcpBZR-br>{&iXF>3&2O1FmmoUUDshI(Ut@12wGlQR!NlGG=sQa3ld5tX3xJk>z zF0uV8y7s4cYLu+Q1MCXbFhF%+hH2@>0J9BXf^08wh*T40wrnrqbW=VL@}qHdhdAmX zjs`H8!|LZ~$?*tHepAfFefII2MALud#4txo&8d4zpj#XUA3chRgf)Rf{R)T}-aDdNn-WU5vO8ZNNUkYI9{01Q3%V|pFUGhAHUgke>+S860 zRg1_=HhcCk|Xgjjdx0olbXJ$~35L`2c^-e=u;k@|xkFV#f8M%7kq z_FvGK3u5_fyS>idWt({2Cw@RTu6W0c6@6)K^gJq&|1rC|jZGw{tSv0PD|5K{rJ(px z)#?WS>F7J;vR(>!(Q%VTg{TUQ&%sE#qYNOHzX?GOB7$zIk`sTg$an@*nGi$>+rz#B z?^6N=5h-ChDFG{mNC+F6l+e@5+b=!>B}SE7<@AeSTGG+Fpa8|hEg?Ew=fPnV zt&ARdjlo5&=JJ0vxlyS@ve7Pr3068|lPTjN7jyM9HNDXoo{acbKgF@@Nh!-vFS;Bc@C*r^d`L&qW{ zXZ!n(v&p^^EP4&e(SFlGI5lfLxstS11j53}apE~trka2LeFe?DcLUQl$#DCr?@}sJ zrdy=qc?%{Hy&7<0)y$(AU1H~l#16|kYUI$#iQt2@yvL-Eujd_iWJgHtX7>phhQ6zI zk+NT}5BbAQwn2g)^Z#XsoZ7K9Hh!?7cI9#3O-^=6z#39waWXS2l_M@Jo^};kA~OZw z*1GK*{WpKg+Mxy<)1*hE_d5A~7c)3`Kx4-R5-y3&d>fyN5wZTpGzVT*Y1;?;rg&M){_FnQDWp< zQiOj@+SHawD?d{Z6Jum7TN_th4J4_4cFFdI9U6J+#>Ql(7|do$qacFA zA94jglb2K>iiI2pOXlmjObBX%h^frNvVAtbb>kvN|Dcsb*C-Onk$gZTZ_}g>Z(P<% z@BnzR!gTS#a6(&ZCP6?hW`S}cngxb90Q7&Nm2P;q;40y7#9hAIVj*g`_+yu~?T)!F zOE@}hE@63}&z<_R)vMM<(P4WvbIM=x1Cptm>NN8Z%NZ>15Bv});2&0P{SK%DJ0yXZ z6qBO2=7ABFrG8hoSONCn`+qRHa|Mrg3fMTAagA-xU$E0XY4|1d@|r5T zf`3@@YVm5RC|x{Vzb6m;4=|f#_XSbL)LlF)TQFK^;tWh1S};yDlZAkPb=hiHwu%>J z2!)4b)adMV$&Fpms>gUtW{G9ZnD1T-BX6o^EN-TVfq#vr^`N1@$NjOHAx_D<9YY3` z#93B1NOu;t!$mEZOvCZOGK{)LHuz1nWer}eMZSKHN( zr`#;wmw$gf0p_~#JPKdh#rw_G`h2r1pVwDalV3O2(5m`tz1gA*f$6~+RioEUWW28w z_M>3~Ubf&aZ4r^u-!YnGM98Ma)#kQrVLQtat1o|Zzv*VwIfdu05L=w4$X*k72bWo07S!XF=DGG0jmnw04j)?5_ZYf^v)$RV@)LR#L^H!Z8DRDoDA$v#5t7qXX~Ft!l5Y@a05ik3d0Sc z>wlp50GQFrcBmkse*?QLU10z&FHPW}L|;hQl$3>YU95~x(*h2%_B2tt z0Gd~j?bdoz=1Ngjl_v?vJxl4i3KQV{RK&XjLkc*C^8LTTj@HhNxC4CH$AX7qZxGmDi^WPXBJqmCwL8R#%-6SUkwU}vbD_JHW+w8+b8;aM6E zl1jpl6Vp{s+QF%7nHSTJSQmt}YJ{|3K}JZ!D!7yw^Tj)}loaH()s@^IDZv5yN0G%`!v=?0+_i$mCrS84pATA7+7#&HZc5Vjq?5b9xuRvSfSO zJ%FczI*+G3ho=(oRK|D;+xhj%>#*VR-Sy?gEn@lsJb}>ynh^91cqKE0>OdU? zQKPfT(2<%6va9KHOh2ap>an7aDd`Rr5fBtwE6_LD5jt?wlLFSIdQb<}T^(4U#{-P( z*^Ab+ncvcwVkTQhnLV>(dw(XpPR{1ov!2Btx+ zNFt?t#7Qg2b_lG)4hTJFnhU0ekI%G@9&9Z%H~>f7VT~B~o@L4wtAESgHMSx}WILS< zeMn-dLL97fkVia@3w}jl5W#!%5j{MwI{H(8AUI1Yx*H@D%>u+P?88#QdD>{sQmXQS zb6$TV>mh7ct&;orB>f@ON)J2&iJh{=1!77nuxbZqpAbl^J0!YODyR;2n}hA)^{1%O zCsK@Tc5S13-(!GeqkmEcIBKKp9d1;s=Hnp?4#u0cS)XaS$ezzMsNY-f^8SeWZIug3 zVd+7wfcUQ{KnUX!ZEcJBd>HOPm8b*tXthfs)TPQ}N?T$m4Lm4g7bWUL1ssCb+6Mq& zcZN;$0LYQ9k$_3nlXBj9;}RXc;~(}RNbgS-S?U2u<6|?ozJHOKW9C&)=*&A4uaqR# zbFQZLd#N)<2lQtwUcy0C)b#K?<9BMf8dWm5;-K}|U^!V)ja7O18lyBsVY7xX=$M`X z1|mP8o=7tk_yOyV4q9D-^qZCZ;(2v_v92b0zP>4^`0~`s#m#EFyIkFFuD83*)(5(N zK2>_Ly4kF@zkikOD`$pWy!a4)x&##XxVF`X zs)`rP1n4u9q0bx(eO|C=UMK}}&+20Ur0z-ja3q@oeSh*O=;IT?o8y4|`*fJ*R+QRZ)M{Ru&QKzB2=ZboDXQTE6;y%joP!jb zo~DqZKAsc>z=@t`=5@-SY>GNyQ&Lw6Ydt}T8;1eOx2bHC!}iG-9wfSM zt!ysN8#J&YqRqO#SzlhQz~nHXmTQs8!_YoElg~rqNl+2Bwvt_Xj$0|Vl>)hd9smb# z{eP!3JEdk}t0h>39;N&T>Shr@P>EMh%aBOuolD`5tg$G)0^W-PchUrn>}PkRN5Kef zQ$VnzSW0SOn_U`lZ_HV-XyUGo_4xhu_WJgEyIGGJg3PDJ$f+mTiE=31U8WKg=|GL~ zYN7)`_mPFZ_$Z*xTlcz+r^ z=<`0rJdD(Q6sZ%|e2#`3BW9`6VxlsLWJFPBJy(q#GHXSY=*1?}3=nOKL}*fh!l}Mp-cf!^b_+}mW z=55{;N<`5HGBkIXHuQ0ZN(gG*$bU4FPM)DbR|-bXAMw=I#aDg6j{aSA<@Zjyw#GpY8V>hn0aMS?Z>xPSaW2^;K4 z_yQ*aoUm0}F(p-?y->(lMwvFZYs`*ODjZr;xTPpV3%3|CZBh*#FMJErs0z1W9=>o3 znEr%%6R|LA;s3TqcuiDsy6gQUZD= z8M{onYI9ipChW*L=~Dw2M1fHrQNs_IB2^AL3por{D)z`>AWfKk^0Vvb2~SWp*|l)wq!Zl9ZHGf`6=ksysvfvCS?( zM4lk7%~XihER$EW!~`|VpJ1Y9tv;4TxHyP{DymKD+rkqutwm}iJM}KnzU*l+b>j4$ zB|M%bX${Q5Rq0nuizIAnK!E}ml30v#_mnf(btaW{7PhRj&^=U36;KD~k`!8GY9IVm zeC>nG*FHcaE6UOb>VM{za4C&)8!8{9x>rb36Ch1ZEPW7pW{GMaexIizKS4dp(Q*b! zx1VPAbW-Yr-2+0GPsrguD8)bNCrRQy++6eGk;T(K+ec5jtA**Yg|S0U(*2Tz7sCx$eFDH(1V$!(;c-*F69#xNsFj6}oRiQFu+YjDOQB?>zML$zlSNjfnmA z35MwtNZdpd+NwhLvq$pN#7%^>#5s3N+(al)(78A!ZsOU&*Df9rH`#k3`M8Pl_p<=B z0U2=FiZ1%&o^cZa6XSo}xQQCI0#f3C{5b?o)X^G7Yss?7HEB!D7=EXR_hg$s{0X&B z%;Gaaqs;Q!jDNwBHZ5MbXj%8}ut$^3>Aju1Ls1KE9Z{iv+(#|+yip6EipghUEi(se zMSkNfYcVe8VXabEG@oZc^6}9cg$G_v7f-eqIPm&=qvROysypBS6K|+=8CF$K%r$9Z@MWo+!*^{4MSuAId~>t@aQj8&_i?@i3TzB8 zeQVdqYPZAPl)4QY%^Sy6Lp%m%k2P4TStntYTKoG*95NFW;0fwJ|0AFrVith1;w@eY z3+$y2MA5WP0&eRb7_c3<^L23c7~8?$#Nq3mj<6m4EQBz}*baLyWHjfBYY@^lI^Ofo zGv_KTr+<9^T4)W_W2-wrcem?pb*b;_?QgGzl=To}C_`;A9a) zH_#^45F;v__a!NIWa7!Ur`F@ebopWGkB8-#D+D+>U=-EKa9dOrHB!XGWmOce@1ed}4`-q*nWZ2_MYxE|PNcrF_%TA|fzTx&FMK@NHTFR;^u!CLig zgMVKibI{#&iNDtu8gO3vee3w~LyW5}Sbn;lPONa1_qT%ZRQ@XP@b5r^Hpl>fc@E$x zY!;s%Phu>t3)v%#sg#}b3S;DAx87i-J^~~a-zPekqX#o35Tqvtf)q+z-AI`|DpF>N z1*DILc~b8vUj3gM9q_heqo*ZCFa#8zaDNwHlE!~Lgs^GXG3Sk>V^Kj(K?RjZh4I)4 z_k2Y=Th~g|i_K*nMXBijt!LuJdUIZj*l+z|UtW5#iwaYaGm`D0x6F``#^z2z!ZXs` zAz6Z*TMvclO6q|NK|uwya?V?4)dZALdnQ!tF*{sNlu`$&9GL$eiv_0FS5Pp))PH3E zL7A5d`-6JAY;5i4yzqP&(0~~o-}mOZ(Yzm|49@plrq_Ui?;QI?m2ksJKBJeZ&gj&f zl5Tla){4E`^hgePKVRC){pJ#>k$XUvlEUvcfV`zVdm93`qSWL$4Q1)|MFk@0uEQ4< zl((6h=H2{l2-IKQDGwS%07y8l(|M{_O5QYnSss$k=aYh1f9ju_u#daJ_d?aT_ufr&f1IPZRHEfe41Jpav) z*y~D2*xn~&8JA zaZc;xBE@WC>`&;`G?7}d$K~VM3Tt`a6?92t;G(_>7C%}p7*i+302!7LwHnei>^Gt30?9yNqhpO54&sagb0H2m#B+l0ti|J?dpj5 z0nEWVeoXja-&N$J2f!4>FcBX<2w9x1R@J-%+xUNUHTt}hfF&pbH8_*uSSWw(U0HJ* z#}R(luRz|wvN4|fkYiU_K9X`pF2~kGDv};xa|OX7!Gs`fS&9F9x@Ql}?DifwNJ+6@ zB#0c$(Z@G^P3xm4-+e1)tL+0mTg~|FFAp9)dGOI!!ps5-R@&K<7c(uHkuxt86VA<^ zoX?)lKie!Xe%-FOXA7m&Ts?n0TWGE4&y>P^DTb(;Q~G_Z*Fj;o-6o~ z*WAzlR$Oh$FF(4yUM;WBKP>}m7xjSK&3Vb~ zt7lxPV#6v)C|y{AkG@hVp%)@p zW`L3lshI#C#IHOmeks=5_7}4ylw-j(4EPeY!h|`@!EN=iSR<$un-9x>pD(xDayu$xHwSId4F&&N z?U;iS1gCsFlVlbMq2Nzjj@ot)u9-ApwnzryX^@f;1r|yQQWazXWeYK{uL!n3bBfT2s4^Yg7M$Sg~ zqW0yBKunRoVoXIRyk|gD1jzoITY?lE?tu|(;XBDoz(s%L8V{FhaxTRkc`i_V6^4;P zJC|a9cQMHs4>rLm3+rh!|CC(MI^8~9dp*C;dXESZcFY*mIi^FU4nGlubRffimJI5@ zyAxu5M`O7S4NorDHx-B1%S)2OTqM_@p)^J@zoS#%5gm2JT(3lEozMt^5-_dOdx=!! zG9{adh2VdQSq#WqbIH<7al5OP;znR@XOVp~%8W*Y{D8#LsO6bAb_BJ2hFaA947e|B z*E%Ff>p=8n1rh|uk+u>z&cPHCIRRBN3?Mm#76DZ{k6~(e0enN8yR<~%PVwOY`D>wK zO8{A^8DDNogj4|z4RDuTkB!YGazOV!qtUn2-Bo|uuoH;n_9l@TA`z|XQZVBuXu6pQ zW@dt>n-NX7Ix#7wp%o}`1O`qf(xctY-QVjGD6naF{!-<9e6cLC7e2nYx>yln1Xr<+ z%C5swWY8xh0HVYNP+Bv@5usJik<$U7$&>^*KanFR)b7I=V)|A)ZqsjHirRo} z6XCCs#w9~6ld|pP=8`Ctd(R{h90zH2G@HGC$Jv@k_GG}V1AnZK4(C8@&wx>=o6uf2 zl-EpU0t|c)K+<)j8*T~kYBDD)7nI-#>CS&Ph2rgY9$jZ4*cmJVx2^Q%lq-EoF0~6q zQZ8yV=YS6juvzO6Tw-kG470Ey^uzh@(5{;#Wo}&Cl(zsya*DQD2P4|*mTp`Fksa5$ zy6ybER1naVnk3wEg2>sHaAy*wFj1gzE@RvB)Cw?oBVazKlO45^4i?7iDYOy+fJc7} z(W;ti8mY`(;Xup9)<&n4dPoTRLSxVn7Fz&iMJ-%C_H#Bn$hA;I@xuVVwde$9XN%Iw zU4Wn}*QS)u_Rj(Afl^YO#=G!c?}G5tfo#EdJ)@L|7zK2Zv{Lm-mvBD1vQ~kw1qd)C zUO+zbB7HML-aX4rMK-dBZVcq;sv~us9E#8x%YNqNFVU&EU_ZQ)A1l$w3g_FwZa0GlX zAf4p`S$9R8ni=Kuv_W5%Nr3Sz56&zK=DZooEQaWdkA&>3r;=f&wN2ODBfEdZBwT4_ z+#Nr}{M7A+V3Gxp-bH3#lL=PW4oZNyMAH5&(bgh3H0ZeXnE>Fg%S^A-$`c7C)9S6`6lof+(Pha!kdP zp4i>vkFPdYH&>f=QI%OdIrD0Mz1(asmN)CG&2}9n`{y%b=gVs>+ra$$a`UFl#y9!; z?_b3c7wh8scC#vf`7?g=YD47wai5WU_i@2TDc$5vR0+ah?XfAhP13R8Lee1 z)w0f|mdly|<3imbU5~z*C56o?oK8fWPKXaL`PFV&LCh$!+^SDc^xBT%l)X z>#zsKb%Pf{=&%G<5qgX%u1vO!^Bo3odEg>JMX!Y7e9F-US~Y)|lkiMPnOm(Yw@;?r^%0K!@>~hGa9xmjB3BHu9^!sv{6UrPWZl%f%qc-Y&72<`T!R|xXi?Tgj&2dqq-7w{(-_$sej?Wtb10Ny66Xj%3ZIwzHZ znashJYj&}k(c+y~q^BpXA1>a}Jd70Y7}2b;T3_5ykqdtj>sb-Vg{la5xqMAs@``cL zOSsy65V`HFvf!-gB=KD1b5;W*{aoVCRVs|C zls#Id{1laPW1{7!h?aQA6hwI)_tZ)Jw27yR37|~urJX>hiIPhCjH1InQ=F< za-kl^$6`JoQ|M;PY_*jAi9&6nc4^C*g}(zRy>`G>fo>Jk9VC4f31 zVhn$#CIRiu7;94+Q1&7yhQXS3)NKybJ-2!2}^3x%J)&;IW(p2KL3 zZUjt3lLx-FK+nq2KlYP;+@?%ij7Q76-*5sLR~DQb#Y8yHa;j#MDkj)^ zDBgGMRn_xS;f}0|R<=u+Fl?zR3~qpK98Z7nW~M0ww+9paKJ1-S@~ortL+a*_(ZZJ3 zEw}@V8_QmSvvmQ?C#CNom=ki$h0#ob!fI|~jpi|$Sk8oxN2F;9M$7(JnI_(?{r|RA zb$^d}nnI{?g>b_P0iNDO(%6${EAc!AYK8m{R&p{>X$K6-(QX=Nw)uPPxy+kb`Y_Z0gs z=b^TJXTB@Q&Fcm2J_+vVLDMfZOg`+K*2S2yarYODt-U8*3CGBoO$1lr!d-(vPy zAdW_d8ubJHh?Qg&0CqUV=IfcL&3F86i6y|{&KXz+fB;0jt3@iNc&JJQ;o~DdK5BT5 zcuk{Yz%E4ZF|bV0mi17o@QdzV)ytZv}MOvbmx&gjYFD&2DT#ZGlii> z%|QFU`K>4Q#{WoR5N06Q2HJxi1Rx}jGXtxcu#PTd*ZwYPkrW8(4oS5#O>L&$(u%`{JBCl~r(Ok>NwQFZ;OPsj9yx09c5C z#}`#nMRt-ZF&14vgQCDe`B=yyHNG!63LNU0u;=ZNkBC_nf6A?(Q&#Ry zcx#&bF}qJeKDRHrlD2KKP@SGpV1)^_UwUSWN?_L<0L2ri1oo${8~uOm++=yu^o%>& zO}?k}%xTnGw&n6YF>}p5-H7JCE0m`=%5DEx;+qH&q61}J&$FcJwMkLFG=5ZoWBd|d zCojvk&|?0to7>H5;N^($K0XFK;^hdwDh|ON^Kt}tVVykY>B!y(8EEGpz?C*LVKq}a zv7UaI^6Eq6uRaoF*e`!blvj&tlVvboRZq&LD_@rv*Q<4L4dNh;ov$v6by+!j`3&}t zeZ<$R>Q`m!ar{`UHwAuj^X*M>vtAYDkK;>r{BT)5h%bl4w&lxm(rvLhuLj3(%>bYNb#s>1PFOzCxz!2o-hPtu_&y35wz|WVrXI`+nIgncchPUwT-Uqpj;^UIp0m$Z`941P_!5;ud zXgim5(@o)3`tkud{sngEDSNYcxO0&jDFp9cDt6k5@abtPWdF^@-ec?=F90-FEL@wI7D&+Khz*Cb54#5gX!PmP}^}0H#3w*C1qqgKIa` z+6rz)xEdCYDeeYJ5;TJ&A1zn)4jZc%beE=zQIk3l>#b9>RCzNUrBLf&Fk%h+krg4jn7Q=YU9=vL*ul6^GF?gzj zR&am##Lj0c{6-K2I|_h*4rYS!9q`>t)8QI)M#cW!P7lJkjv_ytNAdw|8FO=3>J)U)=lT(Y^OS7iJS!u+nZGJ>O`_jNEvkm~d|M=-KAG?Z?OS%h#vF z>1?Nz+Ny_VJAbY9_OVj>>8s<}PHZpE#P);_PcPx={N@H%>aBv0yykxU=l#{O`0^*O zt}o87pFJr4_vsJUhttjB{8+623w(KheX~EFJ$dxiz0V%q`}aKoyW|^D?TQDcg4}%n z^4@n(_~se>>Z=WhkNoDRxbWphD_G*-@pAL+y}u2d(|bkO}L z4a|ADNq-hS=A09+i%;`jcO+hCfOIN-U3D~-fx@GuphU6CCy{Bi9@W_E9QnEwMUHXTuxIrqm#nZ%%6bWbKg+Do(D&ZE-mPuzHp4G&SI^~B(09VR z;)jJF9VCFR^s3(4N*FkHj|WU9YjyG-bv_V#7k|Q940P9mn5!(wH3LPs18izjt4w{i zlg3I?=#*#DsQ(kG%XX}pwt>KV%9W0ZU?wx=Ety>R2~D4plz&J;OA6AnfxiUq0BBT{ z0%d)*d&3Ec;Gw}b8b(qSu6ToS07D8M_!lU5feCLDxhqz7t)Kv)+SLnXmsLFYYGJc; z;C~82i5(k$q6fczB?c3y;l`W_z2s2Ru@J-*a)8IGx$dV&4T_)#??{A< zB9_XQ&m38S{y9(sU@4!wXeqFYIVBhmHGfDoP@MCXZ@wkwjYkFvzTDA2h#l=XFr0}l zxRk}RAG>c;tbP}DEMVGBaNzS0Ljdaw512OnvgTkJC~xagRf!?uf);RLK-MZq&N3eC z4C4Ms5Z8E!)j;(qkhO`l)o+isp`W&ZGcF6#iZF?`y!$eAbbx`RVV=w7`qTjrIDfIR z8UkQ%mgv(O5(kV<(Wi2%J~bJxTCTYkGS`NQ)lT6R3Nht|BW-V`Udjy|JVUb@H`ovc z`2kJ@!oCte0M3~O4`Mk#G?4C?A9SWZg$7H+VWA3uxpL*j{^}*>K)l(0vp@W>Cp02} zx8Ovg=5&cp*(h|H9ll-mJJy-gOn-9?=vwfT6tI^X5Jqt0fJv=H4QL0gDdwwGj{Wp? zH7GF56&6bDhk|md;I7~>h6$l%{baJJz)9zHHd$g|b9o5ecH1PAJivAgGiH#jAUq3F z4*PB3CRlEm(|Q?Az$%##i6RFzqy(4FavxKELtBs79H2=BNj5SlsYnD=41Wj(>Jj7G z2WZ=Iush3{6J0Mo!ktQj3vc8k?sUv*-H(YH)J*O?65OdlPx)osseqSI%TD1=#O45Z zDp1Epnf2JykFcjws5<=$?Abu-vS-V=h8Pml#6V_IC0#x$GcFRtPBQrb8cV9~i8I*- zQ=tXM9C}zD0g&;)WM=Tdz<;PtyJ43lf`Xq)&WSnhDADNP4N)H%JA|ezwiAGODa)8m zg04obKZHO9eluFeDG1~YxM9e~m!M`Nu+R50%YtK&WAF|#1Qyu~OpO3mi~tV;X4CZK60 z;T*)$4)zlS`t^VZsoFWObn9BjmD3oibX12hWun0yXDHC%%83~q^>x=+TBZbMAwm_W z(@8|M6v?6)IL%@ugGbXjPCq0N3c*Vup##aN8Vz8^ofvdbFgL)}1dMW6=v{UI*FmU8 zl*J{NR~KE33XJp&CVz2#6?zh8wLmGDeD2!$+uWCd-z%o&kcG4{$Te8^?&^2IVB-;} zR@NqUzYva<0^k^MR%${EN6-giP~5yVx~+FX5y*h)c}y6)JY6GttEKpwheSc&Y39Mu zXd4(8gF=IR?|`L>!=)eqh0@2LAbUd~V8@Br5g=d}ayaYR3xC2x*w6L+gY>o}XpNcu z(oy{Q@^sa%^k>KhDK}=#L*cSO=T#$IiP1shli?`phIdrSv1Udt+R42D?J2{hFcY^ zTK?*v>`9?g7bnGPW$7t^>=m%&7q>a^O7crW72FEddG*_40pp5&@b>>r9I3#z}DOkrUxW zAqMr0!l@j?X6bi3pmS`ZBt!!>hHUe5eq3!u%ZlbYLGxOYzoWzt&a3McACSbBHA2M` z0uvd8ve)u+RECrmgkVl-HTOuOb0p82K!HnY+XAy4%`!gLTk}Cz8bI}c=Q&cf;Fzbh zAcZEHrUicq@(L2B_+1%rs4fB^90AV>`($~|T3nFMkFhqz!Gkg9XC-=Y3YE@+hyz)w zHW&(*8eLGo1}-Z|6fV2Sgov`ru}onDNk!ix?r(*ySCH0X1JL|FV}mIU+S}v=N!29K zsOlBaSwot_36|i5er4FjK%r1F3@DN!*eZ}vJUgcYRxi!1oaau6BD*0< zX@_M1p~3W*0G#SFN7k#!qqAiP95-Ya+3M426?hy#99FMFdS)TYMejVAB?X=ulD08@ zkugG!BqcMI@bt}3ls_&Ns7^7005OIDIigrFEEiavT#kSW(rg5r4$%b`uAK3}_(%Bd zv%`PB`1JB{d~qrsBd+4p^}b4lxb4m9v_IS&&cya&e=NTI#r6L9riiYtZ%R0CUX?(K zDC*|=yve5A?2jej(pTE-LWtcHJ8Z73Qo84u`XQOs2;Ww2JXi97n@-m%rZ25Gm~PN= zV)5oa*)fWFD(oAz+9&E!J6=4L=^cDf&98s%6D={|C5(C{!a!IBPP$TVtXe(BH8mtr z7prNe;WDI5Q)eq$jV7MgN`aHrn8ce*dTRT}e`Zj#1;>Ltq}uSqDKbj=EuadF6)Rx7 zfix4_rN~?!_D>HuS;p}HzMOfI-fj0kmmlp96e@ycMh)fL(2COeww!uWxfG>6nZ17| zDEXSSk4bmHgJSPpBI$9}FmC&t~mPOMpF6n$XMg*@rfOd(zzE~zm@tz(P(Z=9uD z=_k-GLd1r2RhiLQUTmJDDmv-2Sr&iaIvSYlR+4yP>T#MV`JqXcG!qtG2ym#(NLz}) z@_Gmx8L-wH7IdE0kbwK7G5yu&qW2V&hk6o4%!H(Tn(Ey-qe;;emMJGE;@#wI-s(Fy zK}FRQN}uZ2U*7zu+ex>R%mT~o;04-F?4_ffIH07DUR)A$XHJ}Id2>BZoOFM&_p-m0 zr)>UnpbJ805-CMh48vUPQuP@b^HxIdBR;vw=bCliW6TxGa=oZ5U{RyeDwe!=$!m*q zd)0@D<^k5+CtI8a_|Q06HMvddK7~05a)Eg;&nw(u(_`Rv1$nC>y<>S34TEG<1??lX zh7amI(U*TOn!%eA7?lRc(*A!g`BtIJq=;3hk+~@A<1o_-$gLoCkPG%HXp^Gzqfsk2 z3*nP_>FWLz!NJ#^!D&w{wT1cY-< zX_I<4E+}S*nz@#46AV{!m3}|brUmWtd1IHWFjSRpT!m#9q7Z*cN${VT#GZM4Yw6bf zN?2kXX$2b~(K9!(fQ-L@O<0VaFu#1g-#o8dinHccKn>8f`f7Z|FK>u<#EY=>t=^#_ zj*>Qi2bsB0v6(-nF5KeOg^H;Q9Ts_Un7gp85>76595^|qE}FYoL|^(sF)k)#FHDiW za8t4u?j2_@+=74X1#mYGdXHo;WPsCRShrX!)sX&|)Dqo>+>_tHUUcEt&uD+e=;~)jPN^Ym>f=5FWMbDuk#Yy$eDt zDESPzMd5!oqOJ&0r>8k2MA*h>(;SJJ(Hwl@=(s0y9qCZp^f?G0@3|UiO~zDr7|3e@ zd)nqA&bKrOp>5TGg-^BZ%(#ieV;Jg(3o)P=>4(F+1kByc*4=VqOO0Hh=>dl59?Q2+ zr6*^YA0V0?-9HV&V8ROh(}5Y2W!mbgF?{t;*y?|pO^xBFJr<${4{cEw?Y`0)^4o!!7X0Rx|}{W zpoBbfN+0A~F%NncM#=lZJkbT77vY&Kudf?Gx8d=|vK8=MLn07vh7ewAoX^j^+VO`X+Ec9=*zL^h(4c5ETXAE&a}(eUnZz zBiE3^8d8^xW4f!j8zx}l)8&(a5UcHv`JetFa)ZFy%{4YZe^6Y-{+dFYXF|Q}S@wTC zjnQ-A3f?g=c}{lH2-9nl7E;UBO$m6{L@58>M_msbGAuYAqx8ZX1lH;Z8A!lt&A1de zg~S&%=2dXOR#$(AV6Yv;cDxYNr?wxKHyaFL8{)$zt@)b7_E?lK-Fy#R+RJg#a&*>k zy67CvX5Tt};*)3|v0cPwB&N9$tCW8n)To8G6K}E6Ez0{oY3?x`mf3X8h}{?GkR+)63+*HFrFCYeQSh!7=8*(xS) zvYsp@p~RhRB;h2Igpmlcm24xM$p*4XjDNBq-7lIRGt0Fb&9?1=$stnGCJ`>er! zXYvE2cY%y_kQoaO@RfsB2ZeczsN(IGzpri>L%>bp% z;Mj=n=RrKlGU6rb_&2PY9Y9$mC{F?>62ZxOP|*S^yTPeeaJm3g`H&G%{RY&Og4$wm zhSc?fvmd~@Kv2&^p5G2GgoB0}aDQ5Gpr;Mo=?8af9(hS^Jr(NL-W0qF&sf0tyQ0w4)FG72RnMNdWwyORW+ delta 19672 zcmV)9K*hh|y$X%J3XmiMG&z&uVJLsyJ=vBU$93=g3gjU^;1N--eW9$JLq$qX>?oE^ ziuSSShoPrA0|~@907gn^=ihyAb)&ngaeD)LMpT~I#8lUE_qF<$uYUivSlsNN@Wsu7 zFaG_>=dYgp^52A61Qx8ci&yU!S~4RSUMMD#{X;3u!SU;bxtw=G}({C;+{_kIJ zckBIOeYGvee+4fWyF;;k`sY`_e)8q3C;$CKz%Kbh9CyV7Q$a5N^8U%Uf98v8_|vZ! z9DeePALGFH3$0*?gU8L{<&%Hk)#p6^+n&*R%>umMGov(ydC^RnP2ogXIOCaheN*s- zv`k1}%|HO%Gau~2*}$Y$71ZzF-CVtWx{`iboB||hX5pMOtSz`_&dRvBsuvfhOA2L} znrTfPm_Auk5^Flk_)KdC&cw-@>U2#hEOYa$DHUh_WKB)1X&lq%ubF=?>5#C2DgkmH zHWQcpnpiP-CeB&$goR)N?Zjm)q$CpnpG#nE1XHkvi&IvT>+AdN_lF+tnY=8)4VTPu zr0xsmsHydmIgZqK$s9*|x?qlqpp;-i>nQ}4sWatI)S2U&c~~$LtV)7lT`8}Yf<+QJ z&eA3gR`^ki|%o|lhbTx~1;2)dG5nggR7k*$5YBFGRY=}hN$wa2 z@U5g{)>N|O^Ww*1z3+vXaxB2`YPBz}Xn+N!bAV}OI{{_^|ABu3SovDPgta&o?O zHO~~#WVPC_2y}l5$)v3JBT5K(iU@M^vHo8a=?Z3a&7Sw$YYGn> zB%bZTJDB4})QA48nxcJXTLHQhR0JLXbR6-(0qr6`wMvF*rnzpNTBY-V__CpW=yW@d z3BaOc!H090&$P%wrewhop>FwG_9d%`yI7Y#Lu(Tt+d+RfS_4anD3B)XWK9qQC@pU? z0u@RV>ju_{<8iBfcZzYa%5rY_jHYzato11=_oc5X{M{Sn^p2Ls&eaH|&hD63HGvXh zg12c?w6|GP?{_4UZKDsP%#zFN0u`TD;86n8fOlDdf4JMe!^bOhG&lQl;P!Y}bcFH4xr}Uk>kz9Xz<@plTgsj9ie! zTY3t%V6{Y3PFGNR9)AY#;m(rZNh0FFRu84Da+z;^qho0n2Y=nzkvu*P+Je}TRLq5X zOOz%v%qZP=D1e?k5$U<0&^*jwz32h!#S+#_=Nu({tYkntGypgaNX0Og%zKoI1HF)0 zbU%M0r{3Le8h$%GL%HFX*Od9{43iDGD1dwBycnP&G?T^U<|!EGcF;VX3%|2kr>q1q z=^;qLcu;*dkzl^zcFHCyB?e&=Wy}Sn;1{c8)EmwPfehp^uq6_srptCxQ*9^TV&%+q znjnH7kpg|6iPnRAooIQ){kyx(&7peiGEaZBf~nPzcvImq_4-n(*CVOk{EVr-wD-_$0ZrC2+!C{|;tG5$P0*Xlctzt8>_*Z)0>lU3kRKUH z0rgmeZ}kF|-u3nRu>N6vK$Emu@&{b*t`O4! z7>yj~jebumX=!`Is+qM$Mpe#kz{-NXTYLL;^e?@j{#2y1_2b5p$C zU9lFlEcohCI(w#$6)6!~6u9y&Aeo7C@jsRibr%nPO3ve_m?G}HaF^~v_ouL)lwI;0 zlbECJ;)?|M7@ODP^ zH=>q{oK6@vjQ$8*3p$2LVF<4Mp@(V7j3v;mGZPCI=u9QgGnF4RgQGD~&w&vT0#m5T zF9!?SrD8+^cM8#WXK-P-HG>)4EUWb?X?iLyhBLT^xhD8S(}X-bf17`8axi~O3h8JJ z$1F>6bIgX)fvlinLEFQ}vBbr3EX8FMvgi@1CXhNYF_kT8tVD7*jbo4mms}ZKlB0r4 zdN{Zw#zmLrj#EtI;7r_LiDwF)iQ$|v3FYa*z5#s5x$&WXQhb~%QO~Oo6Q^dx2=tpN z(L6meaO55rD>Fy)J}Q58IXay(BJMYUJ~0k^4;PCarv-*UF)yC|sZbrPyF3jLcGdr` zl!d{_HwsMS)Fl34q8qD$hvmhIU-7ZIvCl~o;@-^>f;SIPQ3BK~2UX~dHJ+8*cD32x zwGyHyM&ws_+q=Wv77P9=o6plWpTMYq4O5K1+I!sZDf3Tg$?$&}JwLAPJkbX6Ao2c3 zi8koRB;R?W4XOXHAGqpJUznlE_WP?rXHt-*$-$nuG`Z;JA~JuLoj~avIUyFw-c#JA z471_?MZhtON6_{9F>;i+kHVD<_Ai7v3WkatAFrzFLj*XKBAPBqS@56O2Sz34Vw}3h zYUoJFjgJP8683-J(5()V`w^iWF@Bai3;-NueS;01mxqNQMxXyT)cLXHOiTj63py+5 znvmic0Q`oUMMlw8jktPyQ&ffIo4fr!R-z*;I$C->*2;y!v&ys1+HHAVMl)eT_-`f| z{0)61(af^#>}$z^o68sB^fWOZ1xFMi1aLGnCbVnEuo-{O%3L;-651NDRX*HPk!2X$ zm<)7I-UZvAlMkx5(+PoN(;y&hrwRhXQ%9!8fwDH^Gc~3!M{iVSw6;_8u!$x$5C5sG zOL*E|9h(X9f3Kf< zC~f5V4ET3ZWhH|uRr!o=^fXO1K^Io!^fgbk6VN_49cGgk%sF>1vtJw`nFi|IQ!pk= zd3x|+b{0ze>0nb@f(cOid(k{k?NeGTzu~ zugO5N!>)tz?P|SM_^$@~aUZ80*N>8LdbB1G18vPh*V^YLWiEL%?9PR-2dn=PJD&Xz zh;4t`z%U>I^cW?g8_G7eX_IO>f4Z?I{E+iQTYgrne#_5!-BUnb0=YM~DeO@Hjuj)6 zv=3sWlI|_$#B4w^sE2y(NP({Vz{|DH!%-uS_kz^ENs#DSNfc#Zl-PY>rl}ivNe1M+ zG?PF+6Xsr%IN>t$9pGqxKsy}#8iC!|Rr`N;`IoYw08igl4`DNRW;Uwtu7a)5K^7VT zC6NUUxqz`johf~@>rjqyk{Bz0Uk1lXo)pZBFmLR7a;4ns!N9_{Q`UB?6|jxG8Xf*t zWXI2=p5J$I0^QZJ0-^80ty|$iD~H-DY*)10Y)9D&v7KF7?I1Ayw{qD z5v9|pc$Gu0Vp8MPFfFk_mvNIPl=FpDbQkI|9SH~x?vRe9Te9f{!W*5O@!+RY=Z{#L`(Fo^}7Hoe)kg$Ch zCW5sXgB?leCaVEDPK8(I*}P~xJA2u|gjKITgJ3RLLKATPggUeku}fby_a)J}Xa^b+ zEV-2eCs(MxF8S&=y^M|WckheCZjEtCx4bQO<&fVO>)WbGWc|MUcT*fb)ORygcS7yf zhXZ|=paio9)8d#&nKKpjdMJNrJxHa~ZQ!#?>Bd$<{#;vV9~&bhqq+}TwR#z@gawHj zE3%zbeX>eo?=aqL!|~z^d5Nq#P9*}Eb;pj-E?Ff;$STv8Rlb#i)jkzfUB$%qqp3#q zFhGn!O2CB77@QnyRJu@7PLyFpm%0q}2~a)WU+HvGm(<=!h?fSBqYi(|`>3Ou>TK$0 z;Uc6lvZKxCx=eaO`SV&yihj~{1m5r#3qOp?tG6y4# zxlDuiFFUTZXaLnL~{_KW8qS zRJys+iZg-A3T(?hUr;ONfKu=iK=_%59#;^HE=70gW<3$SWpZCP_XDKSFqc+#npa4B zhOKPbsOz7!5X(Pc-TmzbKg1w-PfwbG{Wiks8}fe&@#HH+pLJv^f*!KL3}LjV<*a2G z3GBUatc&GzU0TdAz*J$NFwJ_`(}f~1P&EEjQ(TcbPDNSjh}P0lN0fGb=?XvnqXxQ( zLL<8R3gTUiBJ_1(sl;(6%G`0EUH%>rp7E{k&dl6)c3~^laNil--C;n?Vs|KhF(!mr z6-|F&(1mKUTZs)@i+k~~dpqq7r48shwINYbTA@fX$4+dSO>Y9(u$65P0gJ0mwak6H(woomNTGI z!Q$uMPlnoCI0WkgpEc(wxlPVJ@12s7{li^_~f9)OHjvKf2eZOM*P(TYr4DS~^ zHelycH)x8~@k0UI4{}ysE8f+jt96p5?Z5Ysb0cRCXGSB*>jr(XW=9lxczEs?`tujh zzh}ke?u-_f1ugz`_VmTs=ie|@IN~(d#f!IvJY9b@k8PW_P|6 zLM+6CfAgi3a`8$C`R2p+e90D<=WMa_4{xsEX?1t!N6LkOS5{KH_{;icTmJazhuh25 z?Zs#1Uthkv-R$l*t8F>{JNWVX_HMmBfBoXyv#(#A{o{-Ql(b+qRMZjSc=6-)*~{0o zxPY&|EhxOQ#V=vtbs+@|G4Oa*{BZWSW}nG^e}(Ps*BC{(kkx)ayuDn#0hst=4gXrP z;3R<5ovnj9t%+6|z6rCuqKdBIAC~;Ic)3)RE}pL6kq7<@fF{AdAj+6}if82rMhi`x z0kB~N<3uxA2>4f*qju$}cvFT@cvwb*9-S|_u?t$w7_Z4Jv8-A1?JHsAZ8eO=!xS-q ze`s1S8s>Z4Uz-`?l&r@wWI;)sW%Ym*vw#j4ja)Jf#{9ATo_@Q3XMvX-BuManD6G_0poW<9GL&}jyL zyv1Jt{HxV=TRyFStzK-EKES3a+=t0BK`ZeUdP z*Lt%>Hv-_n8C9#-Lu8Cs3ixQ)fR`halN@K$C!u_JW90&MsS=* zXVZ}ziUTmF0OS(|zZ;SqFp+8mM=2O%#%rdM7TAiV`)BFyxbc8VQ8C{aB}T)seV@r6Gda1d@cD3}7eX z97_Ap`X`ZaXi5d#0MW9-a6@3Ke*qfcAY7I05J5uz29PXWVL-~+TDArv@bXc?>>yM` zh5d)&y#jXjuT6~Y6g~k=#X-7_1E`1_0aDfQ?%@i;HdM0G-X4e}lQH8S@Ai zn-Rbd5rF+Plk{|S2=Bpwp$_y+P}dk5xCA*WB6R}XQmGTJ-2x1>{)VI?v_Z>Dia?PZ z^h0C@B6)L!?DZ%<;FNh*)|7`(s(R#%EC?8XMwCd+QmPWMfG3j5j@lCOJc~El zRu0$-c+}0Hn9f-%;NxhJe<#pzG#8syP||&rdcz?xKM@cGu|^(D(4Z>;qtTdP=LQmc z)YsJBz!X7Ii@c%+ePNv_3aiphzA98I8E*FuYxfA0d z(2sYzfPOIIVMI|jfq14$Lp4Y|tcb?M#FO<>IG8nhPbX!D@beh@e`@6o&hYs5=IZhe z@za*zs7bKeU}6x;a@1XugfS7hYw$xj8doee_rm`n?Tj2<&aezeGaM{m(BlEN_1r~k(#)eYrkD{&W)x?33}*riXu*zwvu37~<1FD* z0g|%shQ)eb6V6RnOQsNUVN$$*QOf4XHBO`_@IJ_pK7$+^e=-n4AY)=Cdw^+HAy_ym zcmULw1HY?-6DdDh0Ln~^mWiS05)3en)Qa>`%17L@H%)OQ6B)^c9`m9FQ^Ut++L#Qs z7aC%9Bay4d$nZg6$`-4u-3_)Q(DyAk8Tycw1=o#*9)mpMbzBGm0)q(NgGcn_c{R}= z`U}BXO3_7-e@p_NpnU-kO9kg?BbcRB>``p+bHgP3?NjN0S-cxJt3k-?RE$H z$7aKuu*o{CABQ)C@xArY=?`d#Rk>gkCc(}>qXI%0f0uZ(+y1sJSZipkQ=+lXnPyi% z78+BRDvv20iAibTK^cb=(QqfoAsDTk3%2#JFC7GOWNReCq?w5lYFuKYcS5;7Tj*n- zGD|%m()bwU)(VS5>vNfAS0w@1?xmBfvIWB!O51Njwx_OO+~6 zRqNW0#34F1ezK}#fd+)^MO{-GhNDV(;ZqTPUa@FiDBvM(*dYR>o=I|8R-azuX zM}WMZ34?r8^tC=>Cju(Gy%ir)Rv((K;7Ox74#>YxhiMr^Y28Jmj!V-SN`wiOV^c{{ ze+?g~pbB*7F-WnQX$mRo!%0zqIMK&}yq;+SDVkG|q8=edJ4T6~eC#wzRLER*aH>(s^>5_3wFWx_j65j_b>XsJoi~OhWUHc*-e;%X3P(s6o>;TiQ!L&i!EGr`VG&%2yS}{^O(d@Z!5vl zbKFa@trp0o^FVO$Hhwyr1f!soIx<^E&z)0@Mx3(N`0KHk1uW?zSL z6cV`Xq*PjG9}m=MPP%mPBooZ_34DDN0b?@)=D=efjpO?2SC>|8rxiR#e}b0+t{s?@ zpdN<22ET6u_HF4k#8aq{N(I=!6EGt=(va23P61FT&1X$v8R1m!zmb8a3NU^(_yAH?uheYDJXjlK%aPE!QeY*zM#@zO08P4W@k7TVie%GVkQ z&HHJb?_It(MSQc4_-@90F-Ow<)4pG4MD9N0VA2@8JcwU&fc8t)=?0L2}Ie+ zjUHbeNTR{{_|FgEZxd@eJLklHAnJrDQL0Ih>OJ5djf0*6;ke`0PmmATbn%x&Vt z#Wh}>0jp^{jrP<8-Zs6hrGA_s6PpQB$IWMl#T10rOVej>q$kRa=#+b4H9M~ zf|*PaXi8L$it(y%)AogC8p+CPsHnIEu&^T+q)!yS>^UWh?=cIfB%Kpcg&LxYfdXE3 z?}yi~;GL={28}=yB3?mHu*kIX)v6$LqC%7hsI6g~PRdoje*^+B8r3y`N8OeO;4Q5# zEsF&sABm6Q>?PpG6snno)!Sd{_5w3i`XOY;zZ_xUu* z+(#EKOpk&GWu!*|23b+|DAYZur;>1Bm-%y%@*Y|g4i<1o z1-2aQQTYF%%smu6@lX_YC^OuXD)s;>m`|v+o>hvU%###b?+16sVNakQuSOZzmz=UM zHeq9WY-4QBiF}C(QlAS~zMP|NPMKYk&L`KTo7pw#f4wU$SWcbcIdqUDXbQY- z56N$MC@htSox49D}u@C~}sy7?;OkEjDfi-(TYJ@!a+|77JcZ7f-gAxZw47 zG08E(t4_cHU=;c)(rDmyuE&>gH7AYqQSCyOf3pkcrJ;JEL0(@MBv>07gqNjl4)5AZ zhw%PlbGv?jSH-Nj^Q}tYV}R>hZU17m+hu~5j-4jos)l$B+#YKt6qZJLt53VY$4oGQ zPiF3aVp0xq3&2?M9fjb%6+zxOZ zfA-zSXl0bYq0eVOn!~;LG%KUhrpI@$gw{Yiwz^bvcembFx8$zg{Ps#n`R?k?>NfE( zsympjF?}N7+35lLO*S!frEAi&Fk-;@NRna)8gSp7TQ4oHc6bIxie7M3buR>M7<0Y7 zxZ0E$eNf-XRCm9IYlhe7Y_VBaw+3I-f7QWXU#+j#p=bOKs~7GRAAvAok*irA8gh4; z_atnRi_YI45)FC?aB2gZ0zP#4Vd{^E<;xW!Ho31}(O7qA#}G9#X%EdBC|rMpE?_-e zm9k_OxI2XOE$9t9Bk^yMB8;j1`pA_&CfsS+)g;|^ZxvGCTvplGx0$$QLq#jJf5(h# zjfMSFTeq8xxx`Kr7Hf?+ygY@^x;-w5_WE`J&daE89qxUIakT}%Pq*O2=2m$lDyUB7 z@750g4wO-Y4)9mpc|qc`{2ZNcw1*CpAX#e;)nR<$zzec6;`;#E1-Wy1XziDYl=RXKO_Wn|8l( z-bK1^sW6^7;lNj%c2L)9)XU9PokOYU|BYwj#d>p5tJrV+VP9Q&wTmiK&@+U;-fI+!;RL%BF$=k=CZbi`xp!Ri2Z6ZSK(v!zVY;kAx)VJX^z&c zsA)AT?%1-aTeHHBShON%RYl{KL~>%$O8&NvrKIq^4MN^hk-f8kTTxo_9^s%$>+1wW zuw93*6DaQ-HO+7HcNS1Ze+)Pka~2UGBplc2BIun3Ja8R$XF=*2x^Nv02T!VYU3QQA z^ZDwyZc;yy20Gla5#KKe!d@wb-+f@?zG&RKFpd~MV|w?&=ncv~f6c`IbVphrNkF< z2=w&w_N^ZuzWDw-FcxY9JrJ-#Y8I@;^6Uo^239_)#vO!uYci8Ix%t1FsXET z;8)!60)B|Nka&4AC_Td|CLx64j!dk((&?g{a7zQxDH7Clp3YzEw{PD^ZGzT!$1 zD^^iL@s>R*@qW4l#D8D3cM$;TIzP%xIuDzQzXY+eG)&i9V;TA$eyvhK&qT1y03>Hp zGXXe=uRJS$DVFQzi`f#&v0!Qhe1%+L!W8JZeE{j1RyCYC0ZY$>PbfkYM*?t%Efh|d z1fT>w4iTR~KGE&9d~>N9e1gQRslWf_MEYs5C{`r|kZI<~G=GR-%coz?E6}_xmamj^ z*X3VD^(npw@548Gab3Rg0m$H{dMuVGREpK-<=?0C^}5`S%FxY$8*~l9zf?Qszy!f5 zAI~J21wbhHY0FXT_Q5riCQN3@AUq91GD?A&l7eIf8GzYBAHYD48eQ|k86Nkl8YWU| z)LgLOEs&*%b`|FOeZo<07{oE0Q_dcFst>3;*k#t&>H4#7ztT3 z2C^oFEJ#uU3^1ir4at(vre)0v0&!E~r<4i=en1!sJ%AtS)gXQVVlLElHh>qkD_#W3 z6zMC(RB%E)1Dqm&_CMSZpx~ef24oB0QeGllM9%S`RDY9mDelN~0pqLCFB!CRsmyOL zCOPB5CUVNcdfH5%lIvNgo2P58=XY7}89~C18G}5>bg0$ngZA$(RH%KN2HH)RIImg#rT>N;mN6~Hk9$c$h$>tIBa*V2t^ zq47EAwXIK>k^!1qM^ULhF)LNc^i(d5`s5=D|$ znS=IxNl}Y5F)7&}S^`n%WVS6~-SiJMdv9Gb-jTnvl)+AHGJ%qX8H7rJs$U{-8XXglX0fh@W2%RdGtlx@d`bspJs#($2UWShIx z!j++Ud{~`G2MZ7wvPjwWCf}1eSijBSNHQ7cxgfH7J;~s>snhvtRX!E(8L>5udMFLh zx^nbWGX5!q=wp#Aol$LI%}xmlK^k*m7enVg88}8is;$#nE?0KI$0sus0`CbZV@SJ3 z^Jg8i$qZTqyK$X_#Yv6efqx!|+|{b@^ZCa#$4^sC&o;1sViIo zllJq~hcbmiy2YT4fr6RY3?Hc7R z16-%Jvf#5Zla1iImX6D5O+;Jc_TYN3qL!4fPUY(!aEQNfchuw(bddM^$u>H^o5L-4 z;=zw{I{Mvyp( z;vKNU6*_8m69}QOZcq_~7D`|hp@)#-$_&jg-eCZjdoB`GbbnGP%%>QgfsYa}k>Qz; zGB;vXhIt`uPiz_dX>JAX%?mNM7Eg2t(pu_~zPkb^+-VzqcQi@&^WF2Bm^|v76)Wvs z!PYFFqzl*xaCDX?rsY1qv)YH#)dxBZ7eXYPIkaX-Hd2^hcaqF}~Tj4j4EDgjc!O89kkD$DCQdQBBbPAN|9;N_oD0(9-z}hiq z)I9|ViLloUUNFh^?&rt~o0V@Ba+}E1l?3_X=4>&4gXN6V0)B#xukupYj*?dk!rNqJ zF!QeJ=%k!5qd8EyW*fR0toV6HdQj5({)!*X!$8H45r6d>i{<$>703{=2o?poP!-@V z=I<#buNViu1l8t)$Zcnp#cE9}^Y6Mc2`>jD+K<~aNSI+O^)XzZ}cZhaxk~u z$QiK@;5CSFywY)HT+JF%TDLc4Whv1$W!S9 zPnALDr+q!kil|b)kzn8^$qlNO_n z^YinY7;U^RuGT-|!`otcdb3*O5CsPdnB3uIhQL&MackLSnrx=0vYg6;{}FZtnrH#d zGhSySxg=BYV2sVS!}w6l=P@PSEZBdTHkYLt{k)_`zD}+Yqp~XS3)dh~RK*BKW=( z3nf2&m;K*eNQcoHT@#pyCJ($dL(j_5ANx@sHz5-j)7IaM=B z0F$-d@n9P>;E5e|5bj&{s_MAja7$K2BY*oPOz5{%6$UqeHx37QJ<}L~+r0sP7xvCE zan|DbK6dkmaACvi7Q8I(n*lz=rXJ==={pGKgdB2VG*iH^n%h`TcL*nzGvSRBX&Qvl zu>V!YiMMP2-#4r7?lF&J2z6KuHcSDY-bm2cqpL6^T)}v7k#K_xz0qkA)4!t#S$}y6 zcAGo~Av*;=hP!8P{1Xpw-B+OJe}Eb9(46cRy^s35YH-JaGx4fd08UBD@0NS{l3Kv_ z?T{}i`h7`}yONyZDhHEbI#+jFs6tts3sZbb+C#j+Y9bA4dXvyrWE3C0K*hAOBm7sD zfS~EWg8DtizRP*2ZQq*j3OI4njDPc8|6k+n@^*}(JBHu_+w^O%m{

rK<2 zt(z>5nx1h7yUBNyo;eO%%O+iZB4)0+BaLY8xO^eAvZ^G7udY$fU6@rAEf7h z00eNQ%|uwuluoRtH-BSpeTe+lM{pJD#d1~Plbf!ui|gg0C_j!j+413`yc1sziM`I}<)rIk zby^LM;h3A%JG>-MF%lToQkus38(j}glBA5(Ojg`tTT|sm-+#w^J$P4;xb8Ir3B$m= z&%3PdT>$KNDFE*8)L&kyJg8BB*-jh4ySzxMjX{PWHdmC&0;#h#OWu_}PfQEOCrU;O z7u~j$n#rEy0$UFzgDUx@rqAc^VS7MiHy7*G<<&(g)#f*6R5%B;sXM$(dl*Z;*+t#~ zRb$K3v|ITB*W|1dq>Na*-aL#RNeh%Mj3;gZ8M z<1#PsPxG5{llbG;Sxp73+*(N{xW~HddgD^3X*L%@B>9de=E+dH!H_i}|3?|H^t!kP zh!N5>>nZbX+W_#4bCZFDQz8eQdBHXfAfwy{+e_drZGX@g8^`oXd9L%z1!3^1vLT<` z23zTz87f#1JKPLKljTq)gO*6GKo|ygx@$B!Cmfi`0o@8PyoGP}KFDnpAD7GyAV~9; z!%QHZ-T?wHUThhnwga;l5u#=Cy`{p+Uh_pW(sG=Jx2tST^xVT!UL{<37QOMqYs)IS>` zvmac$zCKu>HnEkYV~V?;dIink$OqF`H4jBz?eY)2*IKucl!|P`3U(YSMs9T<0dZfo z;PUFDCRf+H8Xre#y9lJr9|1vw{}ahuCIV@U|DGQ zzR1?Wb}W}&i7K&GsZ=B#C<~%tQD8!lrNz#_=e?e-d*;mo&QOXSU&ImEc+>s%wfX7e z@Bb=RXNNm{b++QGZ|;2g_|B&fg;@m_thB4gFIQSJBUfH1CY)P6ezAJ8{$hW6{_e0l zoNSa*Yjyu*f1|ZtKUGRUzuup0#QN++tPl9`{2ZQ6udZ;VUMu*>Ywp*7-d^mBFMoM` zd3JjF;$HE;uYS7R9j~tL^^e+2il-eEs;&zwZdxC0~hZS3EEk@~by-;p>%Fu*AXR`Ra!|e;YWbe|1d5lXHeirHh09u-z3K+n-3k zzAm?Q!M2zNr6!1s9c_SqA+O9TIupoT#-B-lhHNX}X@R#KRzOpPh<%S!thg-1(4iDH#cASnfp8K?)u`(TxH^}cTz zlLR^;f62$*t!?c#!!K@EAIqnp?}T;54+}p!NB~{wRlT)^FtG0)5135W>f{sZd?5BN zgrykhwgoX)S(0l8if{wi)TUOM`eY-Gm88%q&!kcRCsLQ~STk({f%lXv9TUM!X385f zx$YC1J|!vtkb;&Jq-O(v3ETnDs3-->`fB%ve-jYFLxXKJjHD=B@do1nh7>&TFHr6R z6W%6rSFG$>K>HQaCoJ=@p&_5HG_Hk97hSpZ zbu}aoE?p>ID7)LY(V>-`c>q@JUJ*oxeJh}VWZZrL+qnTRF~H9y#nfhE8b8C0ITd=z zf1#vfA&4pD0FPC3-A|7i6hRN(kq8+@ER`*vIkE!%bD##mQa*RlQeYKxN-!R3kZPbf zk5|6=mY6pl86@~}NBxZ+Vsns zgJqz+tw&WQhKLJVz=Z)>s~|bcc(6whfA?pCxW+@Q2C7GatWBh?{&2Jn{j>#~aaoX7 zgh{mJ-It-G0}Lb$^IXo?rw(|)iIvq50DCh>pVp8#V04N;l~eVp$#B(j&9#uZHcYH` z3a?OzDL3qCdn@%^Zs6b7p%DSR1t$_Ur%QCoN}<#2@a?kSvCf=knrlGUf}f;- zz0`m(f*S`+Y9(qwJ7`TYU!`*Fr?0C)fnlz&P+~t6lv4$F1&1+A2rcU;lSKtiI;XSA z5(AsdL+G~KCYj^`wquwvgKP!ie_4=n*lz_1&6gj9NCAf5!`SzS^`CevT za13$`-a&@IB71?U5x|NOf8ar&9E8lqV@7a{?Me#26Z4+JGqp;S8E8o z!bHlI9^nwbgVMHU0_8weDkqL0-J`BmvP=mK_d^vBbISWijhw8he>0a^!~we1f}+b1 z_Bnwq2mxS2!zrEmj9?6%7&P-3VRJPBT^tsAm!Zpbu%!_namo3`Sr=Ub<0XTsP+tXb zgmEem28NTnb`~`E2sjFjmP68EW2k7bdfe5LfWgMDs+P2;P7K1aQUDwSCcjoo!V&a= zNDen|jc#i%5K$R0f60w$SC=O}L~qRzUvr-*i#re-P}kZ9#>JpSAX7VFsp4=c2tc9q z@h1q@5D3_@vo(GQ5U>k5oIC6V;URbiy>#?JdJFqnV}87Jx4t+(T(s-u8L~lyjXACo z@QNtaqZg7@lD;~<{tv7zT+fA#%(`~InN`s{pHt|meW zjxMce>MPM%0OMM^4OGnm-8$pR(p$c3ofSn{X=gn;4XR+(@>l<4@7aA~ci^B2Ri|4# z)h-de=~i_}=eV=AM^GvRVC~dd()IBlb#+hSho@)d#92F)v-`weE#uzZ0yiA4wpY8e zg6^o!cBmH0e_oi^7yFB=i?Ze94RXP0!3&4&{zdYYUHnq{ogKx@0we%me3Sj>N-XeJ zQ-|Tacsn@UF;H-h#IiyYP_x4|9Dvv+JdW?u-DsDhwM$R(ecWZ@ry_RoizWXncrwyv z{Qu=Pl4cv5p@Llh3!$&Km&O0S-M_egb+wCB3}THUe_e|AC4~S9@O4`x^3EUAH2zR* zYMp3(KaVbCBXWQT%N-LNrig z$TmOc$JJJ}tZ1$iG_NK32_=4TUR|&Fj3lQSQos zLv;}V;Rtw6*lo&d*5ZP6evGv#4(^RPKMT==Q>b(nL>$OcHIq=d)aZixC2(0mqHx(o zCPb7~_J3mv8%Qep7IA+IY`ucC6dQo%_Zb^ZanL>_CrB!@k49B5fX*7y6i%=NC-f`B zE(QvPl3_rR6v2XfLXlVJr6wKn7rpaf=6{q)YDn6~^hL%9Ig*sjRKoN3Zzz9U zDo~wb1OZ|U0dhpKU|24&#y1}U6{MpPaM(o`Sh#Xh0^=Xy*DrS4;?wip{?(y)jJS$V zm)j~8;?`G(!*+MII}z)%?Y{W(H<#P}`y#r!yei?mzb=6kQPkDtX_HO4+U`rhrLVNw zgntlw5H{GNSmkR^G4(?-s}a7f+<30!0XLoAPfTB0Z!q1U<-`)mU9#^I^HkV(vjFMMdp0BeZIr_EQbI0 z<>Zj`ZoPe5eze_Ds0fxBHI#2dD@y0va_ULtQk3>&_L`vN5osTj8vDIs{|EMhQJF}^ z8g>~?MD9tirl>VfpV~SKJ5#cet#n622Q@Z(bR6&N0p7n|e@u=n117tbB%YXhoF+?lJaS)cjJsEMSoLRrktFJcayVut9#o76;)3teX3u7dHyP^43be5w2#ypKB)6V-~PR5scuSOR2m#h z`!|$K?@+ag497S*r%XPip~e4R_-W-kD8oTRY8Jk!9G+yznLFI z3-In2z+Vk1#h*HIS}qTnLVwiE$yDHd!Y$Y+aAOpBDcH_mH5m4%l3 zB)Bx*#zu6&$IMhx0SU)8RezY~;$&(!OlxH};6tnXQWqAC*Y7rUL1of4gur3}D%F6F zB~qQaXw88*>&N!)I0ON1iOtuLh~4M)yP$Ns`_Bv4lVTK{PY_2(hJSPiXRcZ4@>5b> z!{mcCRXzf^9rF=Ha0`aTxkb_tc0w9L3}qn#^G(lklYVHWv#gRIAX*2)*`7NKTGqw4 zo2ok5H9uT07Ng~2KTy>K5nd*NneFMzvo zTzVvXAp@Ki!@Aj8sfP5wq?YJ5Ne!$$XTSIHDNda!+ir)a+Ec$i3?8sR^t1z-MchZzGonBlE1YB-p2ZecM`uCU z;yR@nnV|}jad_E5Z!Wm0PTJeZ1@l|a1#d*(FbG(%B!7foU>Ia^juG=YMsZZZY5|U^ zA$2*%4>8P=*7!*7QuO7wGKHTQM)cehziojAjFK4&yZUbZX)W65OsQ* zLqddYd^XLIm>JE%CytJLGS`s~wN0Oc@bR{&f!1V9b%%kx7O4JWqL$TgH6V2JLqeEU>-a)$XHqS?{?(;y5c zEYLq4m@!$Vt)3dgSHHnl*KBGGKkc!AJTPZ&iDsos1PTJh*KkRv4LK9sj}4AF6C)C8 zaBQLAPBas)IOV43c`Ic=JJ*7+uj*&uirYf7!GF(0v%&uh)F;0vr#<5*mDdiBFE7r| zs>jpw^8-aK2Rz@n8gEHCPUEp~Up2_kOxB+w<9`F5H0N*tv0^w!|;iblTc;eN%N59~L2sKl)vj;vK0_A#y zyRo4YL@r*Pk9RKlSpjhc2|`b9mu%O4HlSp(+1%fzlIaPG%97Q{^aq48R){6YS3ye1 zC#M;K#e$+EHPYk~R<3UX_v6v4>_)FdEPnz~QSjZ;@6oew(rISo5>i-0>XLCxcNKTT z1WbIod@>MXwe3Ft13E-*5Lmmp#^&v3#f9eYD71Md)W@D>&(jz^7p~wP1C!@uCyg+@ zBWWSEY~7TAcTI%yuV&Qsz#+qe<1tFlyg^{8j*x)_tk#T6fm29)R%2cT2W)k9n}7dc zJBaOgA*N4l-!E@A7{WHhhfP}Z9f|F+C}Fz!9=Q6Jh&sjxRv|3Qj_Px~Z&cL9|D- zJALRn(SngmuZ}3W_HeO3T#gbCwrrw^ddw=>5RQRjbS z0I$7H{v=MGE8q1dF%=lco0k_#o0-ieuG%+wTH8nVweue@Z2Q)D-GBq_g zx1ojtOBGK=Fh({oL`5|?MnW?%I7BuvH$gB)LO3`-lg*ep zd~o>xZ(n}2y6@+DZl#p^YbfRJNSw$hB1DN&CdCv?W)puhhfE;xWFA>W5=atR zKo*ij5=Z8WQT~5k_ghSc5JQw(s;qlws)5u#G8x;BzH zh*~*-GpAcY#$k|Y25WuEYq0JuSpOSr_yMw5+xQG*cY{s+Ag38@P6t~&$RDtkujF=u zymqjyNN?#(T!<@iBcsU};!egA58_F@$T%{dcoQE{+be(2G(QRy>;XHfL16FCDL7c8`vs86B#;D&I@E~O zvR+XB4OEywr4y)10@cgGkql6?0$75`D^Oblj+TJB2v8pej*;Wp;6xQ@cn41Mkk+4| z@iSBxd2?@)H>?G z)fRBA2wd+0oi=bIAKY98ZsmfmP|zI?Zo7axKHzR7=y3-3{K0)k@*OZOFh!?n zBDOr8ri=8Mb&3@En5okYF 0$. @@ -57,18 +57,18 @@ und $\mu_k(U_k \setminus K_k) < \frac{\epsilon}{2^{k+1}}$. Dann definiere $V \coloneqq \bigcap_{k \in \N} U_k$ und $S \coloneqq \bigcup_{k \in \N} K_k$. Da $\forall k \in \N\colon A \subseteq U_k$ und $K_k \subseteq A$, folgt - $S \subseteq A \subseteq V$. Weiter ist für $k \in \N$, da $\sigma_k$ endlich und monoton: + $S \subseteq A \subseteq V$. Weiter ist für $k \in \N$, da $\mu_k$ endlich und monoton: \begin{salign*} - \mu_k(V \setminus S) = \underbrace{\mu_k(V)}_{\le \mu(U_k)} - - \underbrace{\mu_k(S)}_{\ge \mu(K_k)} \le \mu_k(U_k) - \mu_k(K_k) - = \mu_k(U_k \setminus K_k) < \frac{\epsilon}{2^{n+1}} + \mu_k(V \setminus S) = \underbrace{\mu_k(V)}_{\le \mu_k(U_k)} + - \underbrace{\mu_k(S)}_{\ge \mu_k(K_k)} \le \mu_k(U_k) - \mu_k(K_k) + = \mu_k(U_k \setminus K_k) < \frac{\epsilon}{2^{k+1}} .\end{salign*} Damit folgt mit geometrischer Reihe im letzten Schritt \begin{salign*} \mu(V \setminus S) = \sum_{k \in \N} \mu_k(V \setminus S) - < \sum_{k \in \N} \frac{\epsilon}{2^{n+1}} - = \sum_{k \in \N} \frac{\epsilon}{4} \frac{1}{2^{n-1}} - = \sum_{k=0}^{\infty} \frac{\epsilon}{4} \frac{1}{2^{n}} = \frac{\epsilon}{2} + < \sum_{n \in \N} \frac{\epsilon}{2^{n+1}} + = \sum_{n \in \N} \frac{\epsilon}{4} \frac{1}{2^{n-1}} + = \sum_{n=0}^{\infty} \frac{\epsilon}{4} \frac{1}{2^{n}} = \frac{\epsilon}{2} \qquad (*) .\end{salign*} Im Allgemeinen ist $V$ jedoch nicht offen und $S$ nicht abgeschlossen, aber @@ -80,8 +80,8 @@ .\] Da $\mu$ Maß, folgt also $\mu(D_n) \searrow \mu( V \setminus S)$. Das heißt es ex. ein $n_0 \in \N$, s.d. $\forall n \ge n_0$ gilt $\mu(D_n) - \mu(V \setminus S) < \frac{\epsilon}{2}$ $(**)$. Wähle - nun $U = V^{n_0}$ und $K = S^{n_0}$ abgeschlossen. Dann ist $U$ offen, $K$ abgeschlossen - und $K \subseteq A \subseteq K$ mit + nun $U = V^{n_0}$ und $K = S^{n_0}$. Dann ist $U$ offen, $K$ abgeschlossen + und $K \subseteq A \subseteq U$ mit \[ \mu(U \setminus K) = \mu(D_{n_0}) \stackrel{(**)}{<} \frac{\epsilon}{2} + \mu(V \setminus S) \stackrel{(*)}{<} \frac{\epsilon}{2} + \frac{\epsilon}{2} = \epsilon @@ -100,8 +100,8 @@ A_k \coloneqq \left[ \frac{k-1}{n}, \frac{k}{n} \right] \] für $1 \le k \le n$ und $A_k = \emptyset$ für $k > n$. Dann ist $[0,1] \subseteq \bigcup_{k \in \N} A_k$ und - $\text{diam}(A_k) = \frac{1}{n}$ für $1 \le k \le n$ und - $\text{diam}(A_k) = 0$ für $k > n$. Damit folgt + $\text{diam}(A_k) = \frac{1}{n} < \delta $ für $1 \le k \le n$ und + $\text{diam}(A_k) = 0 < \delta $ für $k > n$. Damit folgt \[ \mathscr{H}_{\delta }^{s}([0,1]) \le \sum_{k \in \N} \text{diam}(A_j)^{s} = n \left(\frac{1}{n}\right)^{s} = \left( \frac{1}{n} \right)^{s-1} < \delta^{s-1} @@ -128,7 +128,7 @@ \item Sei $A \subseteq \R$. Beh.: $\exists s^{*} \ge 0$ mit $\mathscr{H}^{s^{*}}(A) < \infty$ $\implies$ $H^{s}(A) = 0$ $\forall s > s^{*}$. \begin{proof} - Sei $s^{*} \ge 0$ mit $H^{s^{*}} < \infty$ und $s > s^{*}$. + Sei $s^{*} \ge 0$ mit $H^{s^{*}}(A) < \infty$ und $s > s^{*}$. Sei weiter $\delta > 0$. Dann ex. $A_i \subseteq \R$ mit $ A \subseteq \bigcup_{i \in \N} A_i$ und $\text{diam}(A_i) \le \delta $, s.d. $\sum_{i \in \N} \text{diam}(A_i)^{s^{*}} \eqqcolon C < \infty$. @@ -181,18 +181,18 @@ Sei dazu $0 \le s < 1$ und $\delta > 0$ und $B_j \subseteq \R$ mit $\text{diam}(B_j) \le \delta $ $\forall j \in \N$ und $(0,1) \subseteq \bigcup_{j \in \N} B_j $. Es - ist $\sum_{j \in \N} \text{diam}(B_j) \le \text{diam}( (0,1)) = 1$. Damit folgt + ist $\sum_{j \in \N} \text{diam}(B_j) \ge \text{diam}( (0,1)) = 1$. Damit folgt \begin{salign*} \sum_{i \in \N} \text{diam}(B_j)^{s} - = \sum_{j \in \N} \text{diam}(B_j)^{s} \text{diam}(B_j)^{s-1} + = \sum_{j \in \N} \text{diam}(B_j) \text{diam}(B_j)^{s-1} = \sum_{j \in \N} \frac{\text{diam}(B_j)}{\text{diam}(B_j)^{1-s}} - \quad \stackrel{1-s > 0}{>} \quad + \quad \stackrel{1-s > 0}{\ge } \quad \frac{\sum_{j \in \N} \text{diam}(B_j)}{\delta ^{1-s}} \ge \frac{1}{\delta ^{1-s}} .\end{salign*} Damit folgt $H_{\delta }^{s}((0,1)) \ge \frac{1}{\delta ^{1-s}}$. Mit $\delta \longrightarrow 0$ folgt $H^{s}((0,1)) = \infty$. - $\Omega \neq \emptyset$ und $\emptyset$ offen. Sei nun $x \in \Omega$, dann ex. + $\Omega \neq \emptyset$ und $\Omega$ offen. Sei nun $x \in \Omega$, dann ex. $\epsilon > 0$, s.d. $(x - \epsilon, x + \epsilon) \subseteq \Omega$. Damit folgt mit Monotonie, Translationsinvarianz und Skalierung von $\mathscr{H}^{s}$: \[ @@ -242,7 +242,7 @@ Sei im Folgenden $\Vert \cdot \Vert_{\infty}$ die Maximumsnorm auf $[0,1]$. Zunächst zu zeigen, dass $f_k$ Cauchy-Folge. Sei dazu $\epsilon > 0$ und setze - $N_0 \coloneqq \log_2\left( \frac{1}{\epsilon} \right) - 1$. Dann gilt + $N_0 \coloneqq \log_2\left( \frac{1}{\epsilon} \right) + 2$. Dann gilt $\forall m, n \ge N_0$ zunächst \begin{salign*} \Vert f_{n+1} - f_n \Vert_{\infty} \le \frac{1}{2} \Vert f_n - f_{n-1} \Vert @@ -258,8 +258,8 @@ &\stackrel{\text{geom. Reihe}}{=} \frac{1 - \frac{1}{2^{m-1}}}{1-\frac{1}{2}} - \frac{1 - \frac{1}{2^{n-1}}}{1-\frac{1}{2}} \\ &= 2 (1 - \frac{1}{2^{m-1}} -1 + \frac{1}{2^{n-1}}) \\ - &= \frac{1}{2^{m}} + \frac{1}{2^{n}} \\ - &\le \frac{1}{2^{N_0+1}} \\ + &= \frac{1}{2^{n-2}} - \frac{1}{2^{m-2}} \\ + &\le \frac{1}{2^{N_0-2}} \\ &< \frac{1}{2^{\log_{2}\left( \frac{1}{\epsilon} \right) }} \\ &= \epsilon .\end{salign*}