Applying to infinite two-player games of length omega where players choose integers, it states that one of the two players has a winning strategy.
This axiom implies that all sets of real numbers are Lebesgue [la-bayg] measurable; and if it is consistent, it implies an infinity of inaccessible cardinal numbers. Incompatible with the Axiom of Choice, this axiom of set theory also implies the consistency of the Zermelo-Fraenkel axioms.  Applying to infinite two-player games of length omega where players choose integers, it states that one of the two players has a winning strategy. Introduced by Polish mathematicians Mycielski and Steinhaus, name this axiom expressible by a tautology in an infinitary logic, and which, FTP, helps prove that many games are determined.
This axiom implies that all sets of real numbers are Lebesgue [la-bayg] measurable; and if it is consistent, it implies an infinity of inaccessible cardinal numbers.
{Axiom of Determinacy} or {AD }