Added barreled spaces.
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This commit is contained in:
Bokuan Li
2026-05-01 16:27:14 -04:00
parent 3077563278
commit 2219ce0b15
11 changed files with 313 additions and 122 deletions

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@@ -66,7 +66,7 @@
\item $BV([a, b]; E)$ is a vector space.
\item For each continuous seminorm $\rho$ on $E$, $[\cdot]_{\text{var}, \rho}$ is a seminorm on $BV([a, b]; E)$.
\item Let $\fF$ be a filter on $BV([a, b]; E)$ and $f: [a, b] \to E$. If
\begin{enumerate}
\begin{enumerate}[label=\alph*]
\item $\pi_x(\fF) \to f(x)$ for all $x \in [a, b]$.
\item For every continuous seminorm $\rho$ on $E$, there exists $U \in \fF$ such that $\sup_{g \in U}[g]_{\text{var}, \rho} = M_\rho < \infty$.
\end{enumerate}