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ANAG skript typo fixed
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\begin{proposition}
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\proplbl{satz umordnung}
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Sei $X$ normierter Raum. Dann:\\
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$\sum_{k=0}^\infty x_k = x$ absolut konvergent $\Rightarrow\;\sum_{k=0}\infty x_{\beta(k)}$ absolut konvergent für jede Umordnung.
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$\sum_{k=0}^\infty x_k = x$ absolut konvergent $\Rightarrow\;\sum_{k=0}^{\infty} x_{\beta(k)}$ absolut konvergent für jede Umordnung.
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\end{proposition}
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\begin{proof}
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wegen Konvergenz der Partialsummen: $\forall\varepsilon>0\;\exists n_0:\sum_{k=n_0}^{\infty} \Vert x_k\Vert<\varepsilon$ \\
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