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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".


Let be a Hausdorff topological space and let be a -algebra on that contains the topology (so that every open set is a measurable set, and is at least as fine as the Borel -algebra on ). Then a measure on is called strictly positive if every non-empty open subset of has strictly positive measure.

More concisely, is strictly positive if and only if for all such that



See also