 Inner regular measure

In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets.Let ("X", "T") be a Hausdorff topological space and let Σ be a σ-algebra on "X" that contains the topology "T" (so that every open set is a measurable set, and Σ is at least as fine as the Borel σ-algebra on "X").