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τ-additivity

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

A measure or set function on a space whose domain is a sigma-algebra is said to be τ-additive if for any upward-directed family of nonempty open sets such that its union is in the measure of the union is the supremum of measures of elements of that is,:

See also

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References

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