Baire set

In mathematics, more specifically in measure theory, the Baire sets form a σ-algebra of a topological space that avoids some of the pathological properties of Borel sets.

There are several inequivalent definitions of Baire sets, but in the most widely used, the Baire sets of a locally compact Hausdorff space form the smallest σ-algebra such that all compactly supported continuous functions are measurable. Thus, measures defined on this σ-algebra, called Baire measures, are a convenient framework for integration on locally compact Hausdorff spaces. In particular, any compactly supported continuous function on such a space is integrable with respect to any Baire measure.