In mathematics, the Kuratowski–Ulam theorem, introduced by Kazimierz Kuratowski and Stanislaw Ulam , called also the Fubini theorem for category, is an analog of Fubini's theorem for arbitrary second countable Baire spaces. Let X and Y be second countable Baire spaces (or, in particular, Polish spaces), and let . Then the following are equivalent if A has the Baire property: 1. * A is meager (respectively comeager). 2. * The set is comeager in X, where , where is the projection onto Y.