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Uncountably many topological models for ergodic transformations

Published online by Cambridge University Press:  19 September 2008

S. Glasner  and
D. Rudolph
S. Glasner
Affiliation:
Tel Aviv University, Ramat Aviv, Israel;
D. Rudolph
Affiliation:
University of Maryland, College Park, MD 20742, USA
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Abstract

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Given a topological process (X, µ, T) where T is a homeomorphism of the compact metric space X which preserves the probability measure µ and is ergodic, we show that there exists an uncountable family {(Xi, µi, Ti)}i∈I of topological processes such that for every i, (Xi, µi, Ti) is measure-theoretically isomorphic to (X, µ, T) but for every i ≠ j, (Xi, µi, Ti) and (Xj, µj, Tj) are not almost topologically conjugate.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 233 - 236
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

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