From 121033cfb66162de42cf15b192701f865a49a165 Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Sun, 28 Jun 2026 14:35:23 -0400 Subject: [PATCH] Fixed label typo. --- src/measure/measure/product.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/measure/measure/product.tex b/src/measure/measure/product.tex index 9e2280d..c6e2f5f 100644 --- a/src/measure/measure/product.tex +++ b/src/measure/measure/product.tex @@ -127,7 +127,7 @@ Therefore $\alg = \cm \otimes \cn$. - Now let $F \subset L^+(X \times Y)$ be the set of functions satisfying (1), then $F \supset \Sigma^+(X, \cm)$ by linearity. Let $f \in L^+(X \times Y)$, then by \autoref{proposition:measurable-simple-separable}, there exists $\seq{\phi_n} \subset \Sigma^+(X \times Y)$ such that $\phi_n \upto f$. In which case, by the Monotone Convergence Theorem, (1) also holds for $f$. + Now let $F \subset L^+(X \times Y)$ be the set of functions satisfying (1), then $F \supset \Sigma^+(X, \cm)$ by linearity. Let $f \in L^+(X \times Y)$, then by \autoref{lemma:measurable-simple-separable}, there exists $\seq{\phi_n} \subset \Sigma^+(X \times Y)$ such that $\phi_n \upto f$. In which case, by the Monotone Convergence Theorem, (1) also holds for $f$. \end{proof}