= Support of a measure
{title2=$\operatorname{supp}\mu$}
= Measure support
{synonym}
For a positive Borel measure on a topological space, the support consists of the points whose every open neighborhood has positive measure. For a finite regular <complex measure> use its <variation measure>. Regularity makes the complement of the support null: compact subsets of that open complement have finite covers by null neighborhoods. A regular probability measure on a compact Hausdorff space whose support is a single point is therefore a <Dirac measure>.
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