From 66dd4b0068c3b7bd98141626520ad0c3b13dba3b Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Sun, 21 Jun 2026 20:53:43 -0400 Subject: [PATCH] Fixed typo in Lebesgue lemma. --- src/measure/lebesgue-integral/non-negative.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/measure/lebesgue-integral/non-negative.tex b/src/measure/lebesgue-integral/non-negative.tex index 445e1b3..45d5875 100644 --- a/src/measure/lebesgue-integral/non-negative.tex +++ b/src/measure/lebesgue-integral/non-negative.tex @@ -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 \[ \int f d\mu = \sup\bracs{\int \phi d\mu \bigg | \phi \in \Sigma^+(X, \cm), \phi \le_u f} \]