nLab
Radon measure

Contents

Contents

Definition

If XX is a locally compact Hausdorff topological space, a Radon measure on XX is a Borel measure on XX that is

  • finite on all compact subsets,

  • outer regular (i.e. can be approximated from outside by measure on the open sets) on all Borel sets, and

  • inner regular (i.e. can be approximated from inside by a measure on compact sets) on open sets.

Properties

(See also monads of probability, measures and valuations.)

Examples

Most measures of interest in geometry are Radon. For example

See also

References

  • V. Bogachev, Measure Theory, vol. 2 (2007).

  • Gerald B. Folland, A course in abstract harmonic analysis, Studies in Adv. Math. CRC Press 1995

Last revised on October 22, 2019 at 16:00:27. See the history of this page for a list of all contributions to it.