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authorAdrian Kummerlaender2016-11-16 20:40:51 +0100
committerAdrian Kummerlaender2016-11-16 20:40:51 +0100
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Add section on rings of sets
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@@ -6,6 +6,16 @@ Sei $\mathcal{B}$ ein Mengensystem.
$$\left(\bigcup_{B\in \mathcal{B}} B \right)^c = \bigcap_{B\in \mathcal{B}} B^c \hspace*{8mm} \left(\bigcap_{B\in \mathcal{B}} \right)^c = \bigcup_{B\in \mathcal{B}} B^c$$
+\subsection*{Mengen-Ring}
+
+Ein Mengensystem $\mathcal{A}$ ist ein Ring gdw. $\forall A, B \in \mathcal{A}$:
+
+\begin{enumerate}[label=(\alph*)]
+ \item $\emptyset \in \mathcal{A}$
+ \item $B\setminus A \in \mathcal{A}$
+ \item $A \cup B \in \mathcal{A}$
+\end{enumerate}
+
\section*{$\sigma$-Algebren}
Ein Mengensystem $\mathcal{A} \subseteq \mathcal{P}(X)$ ist $\sigma$-Algebra auf der nichtleeren Menge $X$ gdw.: