Séminaire étudiants : The Banach Tarski theorem

Mercredi 14 mars 14:15-15:15 - Michaël Mignard - IMB

Séminaire étudiants : The Banach Tarski theorem

Résumé : If a group G acts on a set X, we say that X is G-paradoxal if X is the disjoint union of two sets A and B such that both A and B are piecewise congruent to X under the action of G. Banach and Tarski proved in 1924 that a solid ball is paradoxal under the action of the isometries of the 3-dimension space. This result implies the "construction" of non-measurable sets for Lebesgues measure which relies on the Axiom of choice. We will explain in this talk how such a construction is possible : we will duplicate balls, take rooms in infinte hotels and philosophize about freedom while playing ping-pong.

Lieu : A318

Pour en savoir plus sur cet événement, consultez l'article Séminaire étudiants