Content (measure theory)
id:
content-measure-theory-176-15733753
title:
Content (measure theory)
text:
In mathematics, in particular in measure theory, a content μ is a real-valued function defined on a collection of subsets A such that
- μ ∈ [ 0, ∞ ] whenever A ∈ A.
- μ = 0.
- μ = ∑ i = 1 n μ whenever A 1, …, A n, ⋃ i = 1 n A i ∈ A and A i ∩ A j = ∅ for i ≠ j. That is, a content is a generalization of a measure: while the latter must be countably additive, the former must only be finitely additive. In many important applications the A is chosen to be a ring of sets or to be at le
brand slug:
wiki
category slug:
encyclopedia
description:
original url:
https://en.wikipedia.org/wiki/Content_(measure_theory)
date created:
2007-03-11T20:26:36Z
date modified:
2024-09-03T20:44:58Z
main entity:
{"identifier":"Q5165061","url":"https://www.wikidata.org/entity/Q5165061"}
image:
fields total:
13
integrity:
14