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Bokuan Li
2026-06-20 21:29:53 -04:00
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@@ -144,7 +144,7 @@
\label{corollary:dct-filter}
Let $(X, \cm, \mu)$ be a measure space, $p \in [1, \infty)$, $E$ be a normed vector space over $K \in \RC$, $\fF \subset 2^{L^p(X; E)}$ be a filter, and $g, h \in L^p(X; \real)$ such that:
\begin{enumerate}[label=(\alph*)]
\item $\fF \to g$ pointwise and locally in measure.
\item $\fF \to g$ locally in measure.
\item There exists $F \in \fF$ such that $|f| \le h$ for all $f \in F$.
\end{enumerate}
@@ -156,4 +156,3 @@
\begin{proof}
By \autoref{theorem:vitali-convergence}.
\end{proof}