In mathematics, an inner regular measure is one for which the measure of a set can be approximated from within by compact subsets.

It coincides with m on compact and open sets, and m can be reconstructed from M as the unique inner regular measure that is the same as M on compact sets.

If a tight collection M consists of a single measure μ, then (depending upon the author) μ may either be said to be a tight measure or to be an inner regular measure.