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authorAdrian Kummerlaender2016-11-16 20:46:43 +0100
committerAdrian Kummerlaender2016-11-16 20:46:43 +0100
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Add section on pre measures
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diff --git a/analysis_3.tex b/analysis_3.tex
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--- a/analysis_3.tex
+++ b/analysis_3.tex
@@ -124,3 +124,12 @@ Sei $(X, \mathcal{A}, \mu)$ Maßraum und $A, B, A_j \in \mathcal{A}$ für $j \in
Für $\mu(A) < \infty$ folgt $\mu(B\setminus A) = \mu(B) - \mu(A)$.
Für endliche Maße gilt insb. $\mu(A^c) = \mu(X) - \mu(A)$.
+
+\subsection*{Prämaß}
+
+Eine Abb. $f : \mathcal{A} \rightarrow [0, \infty)$ ist ein Prämaß auf Ring $\mathcal{A}$ gdw.:
+
+\begin{enumerate}[label=(\alph*)]
+ \item $\mu(\emptyset) = 0$
+ \item $\{A_j | j \in \mathbb{N}\} \subseteq \mathcal{A}$ disjunkt und $A = \bigcup_{j\in \mathbb{N}} A_j \in \mathcal{A} \Rightarrow \mu(A) = \sum_{j\in \mathbb{N}} \mu(A_j)$
+\end{enumerate}