Fixed regex incident.
All checks were successful
Compile Project / Compile (push) Successful in 27s

This commit is contained in:
Bokuan Li
2026-05-05 02:00:05 -04:00
parent 0f2e69d1f9
commit 97372173e1
78 changed files with 172 additions and 172 deletions

View File

@@ -52,7 +52,7 @@
\begin{enumerate}
\item[(a)] $f_n \to f$ strongly pointwise.
\item[(b)] There exists $g \in L^1(X) \cap L^+(X)$ such that $\norm{f_n}_E \le g$ for all $n \in \natp$.
\end\{enumerate\}
\end{enumerate}
then $\int f d\mu = \limv{n}\int f_n d\mu$.
@@ -77,7 +77,7 @@
\begin{enumerate}
\item For any $x \in E$ and $A \in \cm$, $I_\lambda(x \cdot \one_A) = x \mu(A)$.
\item For any $f \in L^1(X, |\mu|; E)$, $\normn{I_\lambda f}_{G} \le \norm{\lambda}_{L^2(E, F; G)} \cdot \norm{f}_{L^1(X, |\mu|; E)}$.
\end\{enumerate\}
\end{enumerate}
For any $f \in L^1(X; E)$, $I_\lambda f = \int \lambda(f, d\mu)$ is the \textbf{Bochner integral} of $f$ with respect to $\mu$ and $\lambda$.
@@ -98,7 +98,7 @@
\begin{enumerate}
\item[(a)] $f_n \to f$ strongly pointwise.
\item[(b)] There exists $g \in L^1(X) \cap L^+(X)$ such that $\norm{f_n}_E \le g$ for all $n \in \natp$.
\end\{enumerate\}
\end{enumerate}
then $\int \lambda(f , d\mu) = \limv{n}\int \lambda(f_n, d\mu)$.

View File

@@ -11,7 +11,7 @@
\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}
@@ -40,7 +40,7 @@
\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}