add proper cupdots

lecture.cls

@@ -162,6 +162,22 @@
 % contradiction
 \newcommand{\contr}{\text{\Large\lightning}}
 
+% disjoint unions: provides cupdot and bigcupdot
+\makeatletter
+\def\moverlay{\mathpalette\mov@rlay}
+\def\mov@rlay#1#2{\leavevmode\vtop{%
+   \baselineskip\z@skip \lineskiplimit-\maxdimen
+   \ialign{\hfil$\m@th#1##$\hfil\cr#2\crcr}}}
+\newcommand{\charfusion}[3][\mathord]{
+    #1{\ifx#1\mathop\vphantom{#2}\fi
+        \mathpalette\mov@rlay{#2\cr#3}
+      }
+    \ifx#1\mathop\expandafter\displaylimits\fi}
+\makeatother
+
+\newcommand{\cupdot}{\charfusion[\mathbin]{\cup}{\cdot}}
+\newcommand{\bigcupdot}{\charfusion[\mathop]{\bigcup}{\cdot}}
+
 \ExplSyntaxOn
 
 % S-tackrelcompatible ALIGN environment

ws2020/ana/uebungen/ana1.tex

@@ -177,7 +177,7 @@
                         $\forall i, j \in \N$ mit $i \neq j$. Damit folgt wegen
                         $\mathcal{D}$ Dynkinsystem
                         \[
-                            \bigcup_{i \in \N} A_i = \mathop{\dot{\bigcup_{i \in \N}}} B_i \in \mathscr{D}
+                            \bigcup_{i \in \N} A_i = \bigcupdot_{i \in \N} B_i \in \mathscr{D}
                         .\]
                 \end{enumerate}
             \end{proof}
@@ -191,16 +191,17 @@
                     \item Sei $A \in \mathscr{H}(D)$. Dann ist $A \cap D \in \mathscr{D}_0$. Da
                         $\mathscr{D}_0$ Dynkinsystem folgt:
                         \begin{align*}
-                            A^{c} \cap D = (X \setminus A) \cap D = (X \cap D) \setminus (A \cap D)
-                            = \left( (X \cap D)^{c} \mathop{\dot{\cup}} (A \cap D) \right)^{c}
+                            A^{c} \cap D
+                            = D \setminus (A \cap D)
+                            = \left( D^{c} \cupdot (A \cap D) \right)^{c}
                             \in \mathscr{D}_0
                         .\end{align*}
                     \item Sei $A_i \in \mathscr{H}(D)$ $\forall i \in \N$ mit $A_i \cap A_j = \emptyset$
                         $\forall i, j \in \N, i \neq j$. Dann folgt direkt, da die $A_i$ paarweise
                         disjunkt sind und $\mathscr{D}_0$ Dynkinsystem:
                         \[
-                            \left( \bigcup_{i \in \N} A_i \right) \cap D
-                            = \mathop{\dot{\bigcup_{i \in \N}}} (\underbrace{A_i \cap D}_{ \in \mathscr{D}_0})
+                            \left( \bigcupdot_{i \in \N} A_i \right) \cap D
+                            = \bigcupdot_{i \in \N} (\underbrace{A_i \cap D}_{ \in \mathscr{D}_0})
                             \in \mathscr{D}_0
                         .\] 
                 \end{enumerate}