# Regular measure

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.

Let (*X*, *T*) 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