From 068c5b0194652571b1d727d067fb0a9d43ecec9f Mon Sep 17 00:00:00 2001 From: flavis Date: Fri, 8 Jan 2021 10:03:07 +0100 Subject: [PATCH] add algebra, update some old stuff --- ws2020/algebra/uebungen/algebra8.pdf | Bin 0 -> 131135 bytes ws2020/algebra/uebungen/algebra8.tex | 159 +++++++++++++++++++++++++++ ws2020/ana/uebungen/ana6.pdf | Bin 171914 -> 171916 bytes ws2020/ana/uebungen/ana6.tex | 4 +- ws2020/tut-ana/prasenz7.xopp | Bin 0 -> 778572 bytes ws2020/wtheo/uebungen | 2 +- 6 files changed, 162 insertions(+), 3 deletions(-) create mode 100644 ws2020/algebra/uebungen/algebra8.pdf create mode 100644 ws2020/algebra/uebungen/algebra8.tex create mode 100644 ws2020/tut-ana/prasenz7.xopp diff --git a/ws2020/algebra/uebungen/algebra8.pdf b/ws2020/algebra/uebungen/algebra8.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d79cfd4c889330d6d37c13b1295ca7e6f56f9546 GIT binary patch literal 131135 zcmb5W1yG$?(>02_ySw|r-QC>@uEBy6++BlPa0~81f;+)og1fuJ&&)gX-TQyTy>I3m 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\frac{2-p}{2}} \xrightarrow{k \to \infty} 0$. Also konvergiert $f_k$ in $L^{p}(\R)$ für $p < 2$. @@ -223,7 +223,7 @@ insbesondere $(\mathscr{B}(\R^{n}), \mathscr{B}(\R))$-messbar. Seien nun $A_i \in \mathscr{B}(\R)$ für $i = 1, \ldots, n$. Dann ist \begin{salign*} - \bigtimes_{i=1}^{n} A_i = \bigcap_{i=1}^{n} (A_i \cap \R) + \bigtimes_{i=1}^{n} A_i = \bigcap_{i=1}^{n} (\R^{i-1} \times A_i \times \R^{n-i}) = \bigcap_{i=1}^{n} \underbrace{\pi_{i}^{-1}(A_i)}_{\in \mathscr{B}(\R^{n})} \in \mathscr{B}(\R^{n}) .\end{salign*} diff --git a/ws2020/tut-ana/prasenz7.xopp b/ws2020/tut-ana/prasenz7.xopp new file mode 100644 index 0000000000000000000000000000000000000000..9fd1e051c93a94731829e6b1b5dc974ec445f961 GIT binary patch literal 778572 zcmV(#K;*w4iwFP!000001GK%@uH;CTE%<)FB9Qawm~hgx4XS$JT5IiZuC>(}Kv+D}K@!+!Sf zzxIc}{@?%jU;la@Zs+}I`)hKZjjo6DzyIn7gjnpC|C@dko6hck{hF_~v+qZVzvy?@ z)pa}jkDr^ThskX>+h2eE-@h)i*{|jGdc6EU@%UnOUEapOCx>19>rKbw&*)$A;4%N} zU&r(8zM4J$W7SR8nh&p(TO1PfU$xa)W;zQRW%2i9Je4TWpXtTPD>raMa#t)jy+$Jb zNXHZP*y28#wTV0#cea^Ew<-2Df70t$CQV+hoz8myTs&{|xa49vO>~ltZOcCn&E`DX zwqDuBLQ8Kd3QOOx!7^^r@z-l^a&~j{(jp};nRjkq)IFXrmQM5Q zx*Zdz;i|t#?Q$J&aop-fbM1SR?BJ0u3~&3=>Uy5);cn1LR*Ey0T5Kw}WU-dZCGUE> 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