Baire property

Summary

A subset of a topological space has the Baire property if it differs from an open set by a meagre set. It is the topological analogue of Lebesgue measurability, with meagre sets in the role of null sets. The sets with the Baire property form a sigma-algebra that contains all Borel sets, and in a Polish space it also contains all analytic sets. Under the axiom of choice there are sets of reals without the Baire property.