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author | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-15 05:11:07 +0100 |
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committer | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-15 05:11:07 +0100 |
commit | 7c66b227a494748e2a546fb85317accd00aebe53 (patch) | |
tree | 9c649667d2d024b90b32d36ca327ac4b2e7caeb2 /pages/measure-and-integration/measure-theory | |
parent | 28407333ffceca9b99fae721c30e8ae146a863da (diff) | |
download | site-7c66b227a494748e2a546fb85317accd00aebe53.tar.zst |
Update
Diffstat (limited to 'pages/measure-and-integration/measure-theory')
3 files changed, 2 insertions, 3 deletions
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). |