From 6487655eb3af4cb29e5206d9bfc69c536ceecac0 Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Thu, 18 Jun 2026 20:21:58 -0400 Subject: [PATCH] Fixed typo. --- src/measure/lcg/haar.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/measure/lcg/haar.tex b/src/measure/lcg/haar.tex index 9148896..af86eb9 100644 --- a/src/measure/lcg/haar.tex +++ b/src/measure/lcg/haar.tex @@ -119,7 +119,7 @@ Thus $\mathcal{I}(f) = \bracs{I_g(f)|g \in C_c^+(G) \setminus \bracs{0}}$ is precompact for each $f \in C_c^+(G)$. - For each $V \in \cn_G(1)$, let $E_V = \bracs{I_g|g \in C_c^+(V) \setminus \bracs{0}}$, then $\fF = \bracs{E_V|V \in \cn_G(1)}$ is a filter on the product space $\prod_{f \in C_c^+(G)}\ol{\mathcal{I}(f)}$. By \hyperref[Tychonoff's Theorem]{theorem:tychonoff}, there exists $\bigcap_{V \in \cn_G(1)}\ol{E_V} \ne \emptyset$. + For each $V \in \cn_G(1)$, let $E_V = \bracs{I_g|g \in C_c^+(V) \setminus \bracs{0}}$, then $\fF = \bracs{E_V|V \in \cn_G(1)}$ is a filter on the product space $\prod_{f \in C_c^+(G)}\ol{\mathcal{I}(f)}$. By \hyperref[Tychonoff's Theorem]{theorem:tychonoff}, $\bigcap_{V \in \cn_G(1)}\ol{E_V} \ne \emptyset$. Let $I \in \bigcap_{V \in \cn_G(1)}\ol{E_V}$, then by continuity, \begin{enumerate}[label=(\roman*)]