Product and Markov measures of type III

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

Abstract:

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.

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