Τ additivity

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 G ⊆ Σ 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 , i.e.: