τ-additivity

From The Right Wiki
Jump to navigationJump to search

In mathematics, in the field of measure theory, τ-additivity is a certain property of measures on topological spaces. A measure or set function μ on a space X whose domain is a sigma-algebra Σ is said to be τ-additive if for any upward-directed family 𝒢Σ of nonempty open sets such that its union is in Σ, the measure of the union is the supremum of measures of elements of 𝒢; that is,: μ(𝒢)=supG𝒢μ(G).

See also

References

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