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Product and Markov measures of type III

Part of: Measure-theoretic ergodic theory

Published online by Cambridge University Press:  09 April 2009

Anthony H. Dooley ,
Ivo Klemeš  and
Anthony N. Quas
Anthony H. Dooley
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052, Australia e-mail: a.dooley@unsw.edu.au
Ivo Klemeš
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St. W., Montreal, Quebec, Canada, H3A 2K6 e-mail: klemes@math.mcgill.ca
Anthony N. Quas
Affiliation:
Department of Mathematical Sciences, University of Memphis Memphis, TN 38152USA e-mail:quasa@msci.memphis.edu
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Abstract

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We give some explicit constructions of type III product measures with various properties, resolving some conjectures of Brown, Dooley and Lake. We also define a family of Markov odometers of type III0 and show that the associated flow is approximately transitive.

Keywords

AT propertyG-measuresorbit equivalencenon-singular transformations.

MSC classification

Secondary: 28D15: General groups of measure-preserving transformations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 1 , August 1998 , pp. 84 - 110
Copyright
Copyright © Australian Mathematical Society 1998

References

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