It has been suggested that Inner regular measure be merged into this article. (Discuss) Proposed since December 2023.

In mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable sets and from below by compact measurable sets.

Definition

Let (XT) be a topological space and let Σ be a σ-algebra on X. Let μ be a measure on (X, Σ). A measurable subset A of X is said to be inner regular if

and said to be outer regular if

Examples

Regular measures

Inner regular measures that are not outer regular

Outer regular measures that are not inner regular

Measures that are neither inner nor outer regular

See also

References