Hahn decomposition theorem
id:
hahn-decomposition-theorem-236-7318371
title:
Hahn decomposition theorem
text:
In mathematics, the Hahn decomposition theorem, named after the Austrian mathematician Hans Hahn, states that for any measurable space and any signed measure μ defined on the σ -algebra Σ , there exist two Σ -measurable sets, P and N , of X such that: P ∪ N = X and P ∩ N = ∅ .
For every E ∈ Σ such that E ⊆ P , one has μ ≥ 0 , i.e., P is a positive set for μ .
For every E ∈ Σ such that E ⊆ N , one has μ ≤ 0 , i.e., N is a negative set for μ . Moreover, this decomposition is essentially unique, me
brand slug:
wiki
category slug:
encyclopedia
description:
Measurability theorem
original url:
https://en.wikipedia.org/wiki/Hahn_decomposition_theorem
date created:
date modified:
2023-09-23T08:23:08Z
main entity:
{"identifier":"Q1568811","url":"https://www.wikidata.org/entity/Q1568811"}
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13
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