Outer regular measure

Summary

A measure on a topological space is outer regular when each measurable set is approximated from outside by open sets. The measure of the set is the infimum of the measures of the open sets that contain it. Lebesgue measure on $\R^n$ is outer regular, which is how it is often first constructed. Outer regularity, together with inner regularity, is part of the usual definitions of a regular measure and of a Radon measure.