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authorAdrian Kummerlaender2017-02-09 21:50:55 +0100
committerAdrian Kummerlaender2017-02-09 21:50:55 +0100
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Start writing _Numerik 1_ digest
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@@ -183,6 +183,6 @@ Seien $\mathcal{A}, \mathcal{B}, \mathcal{C}$ $\sigma$-Algebren auf $X, Y, Z \ne
\item $f : X \rightarrow \mathbb{R}^m$ ist $\mathcal{A}$-$\mathcal{B}_m$-mb. $\\\Rightarrow g : X \rightarrow \mathbb{R}; x \mapsto |f(x)|_2$ ist $\mathcal{A}$-$\mathcal{B}_1$-mb.
\item $X = W \dot\cup Z$ mit $\emptyset \neq W, Z \in \mathcal{A}$, $f : W \rightarrow Y$ ist $\mathcal{A}_W$-$\mathcal{B}$-mb., $g : Z \rightarrow Y$ ist $\mathcal{A}_Z$-$\mathcal{B}$-mb. $\Rightarrow h(x) = \begin{cases}
f(x) & x \in W \\
- g(x) & x \in Z
+ g(x) & x \in Z
\end{cases}$ ist $\mathcal{A}$-$\mathcal{B}$-mb.
\end{enumerate}