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Falschen Index in Kapitel 17 korrigiert
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rk-kit committed Mar 5, 2024
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2 changes: 1 addition & 1 deletion Kapitel/Gleichmaessige_Stetigkeit.tex
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Expand Up @@ -173,7 +173,7 @@ \subsection{Punktweise und gleichmäßige Konvergenz von Funktionenfolgen}
Geg. $x_0\in D$, $x\in D$.
\begin{align*}
\abs{f(x) - f(x_0)} &= \abs{f(x) - f_n(x) + f_n(x) - f(x_0)}\\
&\leq \abs{f(x) - f_n(x)} + \abs{f_n(x) - f_n(x_0)} + \abs{f_n(x) - f(x_0)}
&\leq \abs{f(x) - f_n(x)} + \abs{f_n(x) - f_n(x_0)} + \abs{f_n(x_0) - f(x_0)}
\intertext{Wir wenden den $\frac{\varepsilon}{3}$-Trick an}
\fa\varepsilon > 0\ex N\in \N\colon \abs{f_n(y) - f(y)} &< \frac{\varepsilon}{3}\quad\forall y\in D, n\geq N
\intertext{Wir fixieren $n=N$. Dann ist $f_n$ stetig}
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