From c26e3fdfcb39f83cdfb8952578b0cfd536028fdf Mon Sep 17 00:00:00 2001 From: Bokuan Li Date: Tue, 17 Mar 2026 15:32:44 -0400 Subject: [PATCH] Minor typo fix. --- src/measure/bochner-integral/bochner.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/measure/bochner-integral/bochner.tex b/src/measure/bochner-integral/bochner.tex index 78791af..5a5d1e5 100644 --- a/src/measure/bochner-integral/bochner.tex +++ b/src/measure/bochner-integral/bochner.tex @@ -30,7 +30,7 @@ I\phi + I\psi &= \sum_{y \in \phi(X)}y \cdot \mu\bracs{\phi = y} + \sum_{z \in \psi(X)}z \cdot \mu\bracs{\psi = z} \\ &= \sum_{y \in \phi(X)} \sum_{z \in \psi(X)} (y + z) \cdot \mu\bracs{\phi = y, \psi = z} \\ &= \sum_{y \in (\phi + \psi)(X)}\sum_{{z \in \phi(X) \atop {z' \in \psi(X) \atop z + z' = y}}}(z + z') \cdot \mu\bracsn{\phi = g, \psi = z'} \\ - &= \sum_{y \in (\phi + \psi)(X)}y \cdot \mu(\bracs{\phi + \psi = y}) = I\phi + I\psi + &= \sum_{y \in (\phi + \psi)(X)}y \cdot \mu\bracs{\phi + \psi = y} = I\phi + I\psi \end{align*} so $I$ is a linear operator on $\Sigma(X; E) \cap L^1(X; E)$ that satisfies (1).