Fixed typo in Lebesgue lemma.

This commit is contained in:
Bokuan Li
2026-06-21 20:53:43 -04:00
parent 84fb052c78
commit 66dd4b0068

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@@ -25,7 +25,7 @@
\label{lemma:lebesgue-non-negative-strict}
Let $(X, \cm, \mu)$ be a measure space and $f \in \mathcal{L}^+(X, \cm)$.
\begin{enumerate}
\item For each $\phi \in \Sigma^+(X, \cm)$, denote $\phi \le_u f$ if there exists $\delta > 0$ such that $\phi + \delta \ge f$ on $\bracs{\phi > 0}$, then
\item For each $\phi \in \Sigma^+(X, \cm)$, denote $\phi \le_u f$ if there exists $\delta > 0$ such that $\phi + \delta \le f$ on $\bracs{\phi > 0}$, then
\[
\int f d\mu = \sup\bracs{\int \phi d\mu \bigg | \phi \in \Sigma^+(X, \cm), \phi \le_u f}
\]