Replaced mentions of normed spaces to normed vector spaces.
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Bokuan Li
2026-03-17 15:18:31 -04:00
parent 37a5ce14bf
commit 16e6beb117
12 changed files with 24 additions and 24 deletions

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@@ -125,7 +125,7 @@
\begin{proposition}
\label{proposition:measurable-simple-separable-norm}
Let $(X, \cm)$ be a measurable space, $(E, \norm{\cdot}_E)$ be a separable normed space, and $f: X \to E$, then the following are equivalent:
Let $(X, \cm)$ be a measurable space, $(E, \norm{\cdot}_E)$ be a separable normed vector space, and $f: X \to E$, then the following are equivalent:
\begin{enumerate}
\item $f$ is $(\cm, \cb_E)$-measurable.
\item There exists simple functions $\seq{f_n}$ such that $\abs{f_n} \le \abs{f}$ for all $n \in \natp$, and $f_n \to f$ pointwise.