Positive and negative sets
id:
positive-and-negative-sets-248-10527439
title:
Positive and negative sets
text:
In measure theory, given a measurable space and a signed measure μ on it, a set A ∈ Σ is called a positive set for μ if every Σ -measurable subset of A has nonnegative measure; that is, for every E ⊆ A that satisfies E ∈ Σ , μ ≥ 0 holds. Similarly, a set A ∈ Σ is called a negative set for μ if for every subset E ⊆ A satisfying E ∈ Σ , μ ≤ 0 holds. Intuitively, a measurable set A is positive for μ if μ is nonnegative everywhere on A . Of course, if μ is a nonnegative measure, every element of Σ i
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wiki
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encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Positive_and_negative_sets
date created:
date modified:
2022-04-14T08:19:18Z
main entity:
{"identifier":"Q3799160","url":"https://www.wikidata.org/entity/Q3799160"}
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fields total:
13
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