From 7c66b227a494748e2a546fb85317accd00aebe53 Mon Sep 17 00:00:00 2001 From: Justin Gassner Date: Thu, 15 Feb 2024 05:11:07 +0100 Subject: Update --- pages/measure-and-integration/measure-theory/measures.md | 2 +- pages/measure-and-integration/measure-theory/sigma-algebras.md | 1 - pages/measure-and-integration/measure-theory/signed-measures.md | 2 +- 3 files changed, 2 insertions(+), 3 deletions(-) (limited to 'pages/measure-and-integration/measure-theory') diff --git a/pages/measure-and-integration/measure-theory/measures.md b/pages/measure-and-integration/measure-theory/measures.md index 637ab0c..c843881 100644 --- a/pages/measure-and-integration/measure-theory/measures.md +++ b/pages/measure-and-integration/measure-theory/measures.md @@ -14,7 +14,7 @@ is mapping $\mu : \mathcal{A} \to [0,\infty]$ such that - $\mu(\varnothing) = 0$, - for every sequence $(A_n)_{n \in \NN}$ of pairwise disjoint sets $A_n \in \mathcal{A}$ - + $$ \mu \bigg\lparen \bigcup_{n=1}^{\infty} A_n \! \bigg\rparen = \sum_{n=0}^{\infty} \mu(A_n). diff --git a/pages/measure-and-integration/measure-theory/sigma-algebras.md b/pages/measure-and-integration/measure-theory/sigma-algebras.md index 5d22f6b..8f58f09 100644 --- a/pages/measure-and-integration/measure-theory/sigma-algebras.md +++ b/pages/measure-and-integration/measure-theory/sigma-algebras.md @@ -47,4 +47,3 @@ defined to be the intersection of all σ-algebras on $X$ containing $\mathcal{A} By the previous proposition, $\sigma(\mathcal{E})$ is in fact a σ-algebra on $X$. ## Products of {{ page.title }} - diff --git a/pages/measure-and-integration/measure-theory/signed-measures.md b/pages/measure-and-integration/measure-theory/signed-measures.md index 77b2416..657a28f 100644 --- a/pages/measure-and-integration/measure-theory/signed-measures.md +++ b/pages/measure-and-integration/measure-theory/signed-measures.md @@ -18,7 +18,7 @@ is a mapping $\mu : \mathcal{A} \to [-\infty,\infty]$ such that - for every sequence $(A_n)_{n \in \NN}$ of pairwise disjoint sets $A_n \in \mathcal{A}$ {: .my-0 } - + $$ \mu \bigg\lparen \bigcup_{n=1}^{\infty} A_n \! \bigg\rparen = \sum_{n=0}^{\infty} \mu(A_n). -- cgit v1.2.3-54-g00ecf