Τ-additivity

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

A measure or set function $\mu$ on a space $X$ whose domain is a sigma-algebra $\mathrm{\Sigma }$ is said to be Template:Em if for any upward-directed family $𝒢\subseteq \mathrm{\Sigma }$ of nonempty open sets such that its union is in $\mathrm{\Sigma },$ the measure of the union is the supremum of measures of elements of $𝒢;$ that is,: $$\mu (\bigcup 𝒢)=\underset{G\in 𝒢}{\sup }\mu (G).$$

See also

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References

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