Τ-additivity explained

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

\mu

on a space

X

whose domain is a sigma-algebra

\Sigma

is said to be if for any upward-directed family

l{G}\subseteq\Sigma

of nonempty open sets such that its union is in

\Sigma,

the measure of the union is the supremum of measures of elements of

l{G};

that is,:\mu\left(\bigcup \mathcal\right) = \sup_ \mu(G).

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