# Baire set

From Encyclopedia of Mathematics

*in a locally compact Hausdorff space $X$*

2020 Mathematics Subject Classification: *Primary:* 28A05 *Secondary:* 03E1554H05 [MSN][ZBL]

A set belonging to the $\sigma$-ring generated by the class of all compact sets in $X$ that are $G_\delta$-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

[H] | P.R. Halmos, "Measure theory" , v. Nostrand (1950) MR0033869 Zbl 0040.16802 |

**How to Cite This Entry:**

Baire set.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Baire_set&oldid=32053

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