diff --git a/src/fa/lp/ui.tex b/src/fa/lp/ui.tex index af2c123..b00c919 100644 --- a/src/fa/lp/ui.tex +++ b/src/fa/lp/ui.tex @@ -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} -