From 21e201d4ff8c0269f889a4555f25fa93eca464a8 Mon Sep 17 00:00:00 2001 From: Anthony Berg Date: Mon, 3 Mar 2025 12:37:45 +0100 Subject: [PATCH] Quartz sync: Mar 3, 2025, 12:37 PM --- content/Lectures/Lecture 14.md | 1 + 1 file changed, 1 insertion(+) diff --git a/content/Lectures/Lecture 14.md b/content/Lectures/Lecture 14.md index a95753ab..829e5d78 100644 --- a/content/Lectures/Lecture 14.md +++ b/content/Lectures/Lecture 14.md @@ -18,6 +18,7 @@ For $A_{n} \in M$ **pairwise disjoint** Example $M = \wp(X)$ define measure: $\mu(A) = \begin{cases}\#A & \text{When}\ A\ \text{is finite}\\ \infty & \text{When}\ n\ \text{is infinite}\end{cases}$ + --- # Simple Function A **simple function** on $X$ is a function $s : X \to \mathbb{R}$ of the form $s = \Sigma_{i=1}^{n} a_{i} \times X_{a_{i}}$ for pairwise disjoint $A_{i} \subset X$ and distinct real numbers $a_{i}$