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Ergodic and mixing sequences of transformations

Published online by Cambridge University Press:  19 September 2008

Daniel Berend  and
Vitaly Bergelson
Daniel Berend
Affiliation:
Department of Mathematics, University of California, Los Angeles, CA 90024, USA
Vitaly Bergelson
Affiliation:
Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Isra
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Abstract

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The notions of ergodicity, strong mixing and weak mixing are defined and studied for arbitrary sequences of measure-preserving transformations of a probability space. Several results, notably ones connected with mean ergodic theorems, are generalized from the case of the sequence of all powers of a single transformation to this case. The conditions for ergodicity, strong mixing and weak mixing of sequences of affine transformations of compact groups are investigated.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 3 , September 1984 , pp. 353 - 366
Copyright
Copyright © Cambridge University Press 1984

References

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