Ergodic Theory and Dynamical Systems

Research Article

An amenable equivalence relation is generated by a single transformation

A. Connesa1, J. Feldmana2 and B. Weissa3

a1 Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France

a2 Department of Mathematics, University of California at Berkeley, California, USA

a3 Hebrew University of Jerusalem, Israel

Abstract

We prove that for any amenable non-singular countable equivalence relation RX×X, there exists a non-singular transformation T of X such that, up to a null set:

S014338570000136X_eqnU1

It follows that any two Cartan subalgebras of a hyperfinite factor are conjugate by an automorphism.

(Received May 25 1981)

(Revised September 01 1981)