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. 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). Then a measure μ on the measurable space (X, Σ) is called inner regular if, for every set A in Σ,