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Approximately transitive flows and ITPFI factors

Published online by Cambridge University Press:  19 September 2008

A. Connes  and
E. J. Woods
A. Connes
Affiliation:
Institute des Hautes Études Scientifiques, 35, route de Chartres, 91440 Bures-sur-Yvette, France
E. J. Woods
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6, Canada
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Abstract

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We define a new property of a Borel group action on a Lebesgue measure space, which we call approximate transitivity. Our main results are (i) a type III0 hyperfinite factor is ITPFI if and only if its flow of weights is approximately transitive, and (ii) for ergodic transformations preserving a finite measure, approximate transitivity implies zero entropy.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 2 , June 1985 , pp. 203 - 236
Copyright
Copyright © Cambridge University Press 1985

References

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