Analytic set

Summary

An analytic set is a subset of a Polish space that is a continuous image of the Baire space. Equivalently, it is the projection of a closed set or of a Borel set in a product. Every Borel set is analytic, but some analytic sets are not Borel. Suslin's theorem says that a set is Borel exactly when both it and its complement are analytic. Analytic sets are Lebesgue measurable, and an uncountable analytic set contains a perfect set.