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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, strict positivity is a concept in measure theory. Intuitively, a strictly positive measure is one that is "nowhere zero", or that it is zero "only on points". Let (X, T) be a Hausdorff topological space and let be a -algebra on X that contains the topology T (so that every open set is a measurable set, and is at least as fine as the Borel -algebra on X). Then a measure on (X, ) is called strictly positive if every non-empty open subset of X has strictly positive measure.