Ergodic Theory and Dynamical Systems



The Radon–Nikodym problem for approximately proper equivalence relations


JEAN RENAULT a1
a1 Départment de Mathématiques, Université d'Orléans, 45067 Orléans, France (e-mail: renault@labomath.univ-orleans.fr)

Article author query
renault j   [Google Scholar] 
 

Abstract

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 approximately finite-dimensional (AF) algebras. As applications, we retrieve sufficient conditions for the uniqueness of traces on AF algebras and parts of the Perron–Frobenius–Ruelle theorem.

(Received January 7 2003)
(Revised September 14 2003)