The Radon-Nikodym problem for approximately proper equivalence relations

Jean Renault (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We study the Radon-Nikodym problem for approximately proper equivalence relations and more specifically the uniqueness of certain Gibbs states. One of our tools is a variant of the dimension group introduced in the study of AF algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the Perron-Frobenius-Ruelle theorem.

Mots clés: Equivalence relations; Perron-Frobenius theorem; cocycles; Radon-Nikodym derivative; dimension groups

Domaines: Algèbres d'opérateurs [math.OA]; Systèmes dynamiques [math.DS]

Jean Renault. The Radon-Nikodym problem for approximately proper equivalence relations. Ergodic Theory and Dynamical Systems, 2005, vol 25, pp.1643-1672. ⟨hal-00080802⟩