# nLab Radon measure

Contents

### Context

#### Measure and probability theory

measure theory

probability theory

# Contents

## Definition

If $X$ is a locally compact Hausdorff topological space, a Radon measure on $X$ is a Borel measure on $X$ 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.

## Examples

Most measures of interest in geometry are Radon. For example

## 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.