Polished A-A and added new lines for broken enumerates.
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@@ -11,7 +11,8 @@
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\begin{enumerate}
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\item[(a)] For each $n \in \natp$, $\norm{f_n}_E \le \norm{f}_E$.
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\item[(b)] $\norm{f_n(x) - f(x)}_E \to 0$ pointwise as $n \to \infty$.
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\end{enumerate}
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\end\{enumerate\}
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\end{enumerate}
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If the above holds, then $f$ is a \textbf{strongly measurable} function.
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@@ -39,7 +40,8 @@
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\begin{enumerate}
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\item For any strongly measurable functions $f, g: X \to E$ and $\lambda \in K$, $\lambda f + g$ is strongly measurable.
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\item For any strongly measurable functions $\bracs{f_n: X \to E|n \in \natp}$ and $f: X \to E$, if $f_n \to f$ strongly pointwise, then $f$ is strongly measurable.
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\end{enumerate}
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\end\{enumerate\}
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\end{proposition}
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\begin{proof}
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