# Baire set

From Encyclopedia of Mathematics

*in a locally compact Hausdorff space *

A set belonging to the -ring generated by the class of all compact sets in that are -sets. A Baire set serves to define the concept of a Baire-measurable function. In all classical particular cases in which measure theory is developed in topological spaces, e.g. in Euclidean spaces, the concept of a Baire set coincides with that of a Borel set.

#### References

[1] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) |

**How to Cite This Entry:**

Baire set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Baire_set&oldid=15423

This article was adapted from an original article by V.A. Skvortsov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article