View source for Baire set

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''in a locally compact Hausdorff space $X$''

{{MSC|28A05|03E15,54H05}}

[[Category:Classical measure theory]]

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|Borel set]].

====References====
{|
|valign="top"|{{Ref|H}}|| P.R. Halmos, "Measure theory" , v. Nostrand (1950) {{MR|0033869}} {{ZBL|0040.16802}}
|}