Radon measure

Summary

A Radon measure on a Hausdorff topological space is a Borel measure that is locally finite and inner regular with respect to compact sets. Radon measures are the measures that fit well with the topology. On a locally compact Hausdorff space, the Riesz–Markov–Kakutani theorem represents each positive linear functional on continuous functions of compact support by such a measure. Lebesgue measure, Haar measures and the usual measures of probability on Polish spaces are Radon measures.