tau additivity

Short description: Property of certain measures on topological spaces

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 τ-additive 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

• Net (mathematics) – A generalization of a sequence of points
• Sigma additivity
• Valuation (measure theory)

References

• Fremlin, D.H. (2003), Measure Theory, Volume 4, Torres Fremlin, ISBN 0-9538129-4-4 .