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The Radon–Nikodym problem for approximately proper equivalence relations

Published online by Cambridge University Press:  04 August 2005

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 25 , Issue 5 , October 2005 , pp. 1643 - 1672
Copyright
2005 Cambridge University Press

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