Marczewski's problem asks if this theorem holds in rotational situations when the Property of Baire is exhibited.
Marczewski's problem asks if this theorem holds in rotational situations when the Property of Baire is exhibited. Its central proposition may be achieved via the Wallace-Bolyai-Gerwien Theorem if point-by-point pairing is required, and the existence of a Følner sequence identifies groups for which it does not hold, which include Borel sets. One of its strong versions is derived from the (*) Schroeder-Bernstein theory along with its primary example, which is based on a premise of the Vitali Theorem and is an extension of the Hausdorff Paradox. It was derived from the Axiom of Choice, to which it is often given as a counterexample. For 10 points, name this theorem that states that two three or higher dimensional non-empty bounded subsets of a Euclidean space can be decomposed into countably many disjoint subsets such that two congruent subsets of each may be assembled, named for two Polish mathematicians.
Marczewski's problem asks if this theorem holds in rotational situations when the Property of Baire is exhibited.
{Banach}-{Tarski} theorem or paradox