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In [[mathematics]], in the field of [[measure theory]], '''τ-additivity''' is a certain property of [[Measure_(mathematics)|measure]]s on [[topological space]]s.


A measure ''µ'' on a space ''X'', defined on a [[sigma-algebra]] Σ is said to be τ-additive, if for any [[Directed_set|upward-directed]] family <math>\mathcal{G}\subseteq \Sigma</math> of nonempty open sets, such that its [[Union (set theory)|union]] is in Σ, the measure of the union is the [[supremum]] of measures of elements of <math>\mathcal G</math>, i.e.:
:<math>\mu\left(\bigcup \mathcal{G}\right)=\sup_{G\in\mathcal{G}}\mu(G)</math>


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==References==
* {{citation|first=D.H.|last=Fremlin|title=Measure Theory, Volume 4|publisher=Torres Fremlin|year=2003|isbn=0-9538129-4-4}}.
 
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{{DEFAULTSORT:T-additivity}}
[[Category:Measure theory]]

Revision as of 05:00, 24 May 2013

Template:Lowercase Template:Orphan In mathematics, in the field of measure theory, τ-additivity is a certain property of measures on topological spaces.

A measure µ on a space X, defined on a sigma-algebra Σ is said to be τ-additive, if for any upward-directed family of nonempty open sets, such that its union is in Σ, the measure of the union is the supremum of measures of elements of , i.e.:

References

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