Added notation for space of measurable functions.

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Bokuan Li
2026-06-21 21:08:13 -04:00
parent 66dd4b0068
commit a57686be8f
3 changed files with 11 additions and 0 deletions

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@@ -1,6 +1,14 @@
\section{Convergence in Measure}
\label{section:convergence-in-measure}
\begin{definition}[In Measure]
\label{definition:in-measure}
Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a metric space, then the uniform
\end{definition}
\begin{definition}[Convergence in Measure]
\label{definition:convergence-in-measure}
Let $(X, \cm, \mu)$ be a measure space, $(Y, d)$ be a metric space, and $\fF$ be a filter of $(\cm, \cb_Y)$-measurable functions, and $f$ be a $(\cm, \cb_Y)$-measurable function, then $\fF \to f$ \textbf{in measure} if for each $\eps > 0$,