Polished A-A and added new lines for broken enumerates.
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Bokuan Li
2026-05-05 01:50:35 -04:00
parent 47a7e1de68
commit 0f2e69d1f9
81 changed files with 441 additions and 185 deletions

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