Cleaned up MCT in measure.

This commit is contained in:
Bokuan Li
2026-06-20 10:11:25 -04:00
parent 242c7ebea1
commit 094320ef29
2 changed files with 23 additions and 10 deletions

View File

@@ -18,7 +18,7 @@
\begin{proposition}
\label{proposition:lebesgue-simple-properties}
Let $(X, \cm, \mu)$ be a measure space and $f, g \in \Sigma^*(X, \cm)$, then:
Let $(X, \cm, \mu)$ be a measure space and $f, g \in \Sigma^+(X, \cm)$, then:
\begin{enumerate}
\item For any $\alpha \ge 0$, $\int \alpha f d\mu = \alpha \int f d\mu$.
\item $\int f + g d\mu = \int f d\mu + \int g d\mu$.