Strictly positive measure

In mathematics, strict positivity is a concept in measure theory.

Intuitively, a strictly positive measure is one that is "nowhere zero", or that is zero "only on points".

be a Hausdorff topological space and let

σ

(so that every open set is a measurable set, and

is at least as fine as the Borel

is called strictly positive if every non-empty open subset of

has strictly positive measure.

is strictly positive if and only if for all