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An amenable equivalence relation is generated by a single transformation

Published online by Cambridge University Press:  19 September 2008

A. Connes ,
J. Feldman  and
B. Weiss
A. Connes
Affiliation:
Institut des Hautes Etudes Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, France
J. Feldman
Affiliation:
Department of Mathematics, University of California at Berkeley, California, USA
B. Weiss
Affiliation:
Hebrew University of Jerusalem, Israel
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Abstract

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

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

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 1 , Issue 4 , December 1981 , pp. 431 - 450
Copyright
Copyright © Cambridge University Press 1981

References

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