Support of a measure ($\mathrm{supp}\mu$)

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.