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Ergodic and mixing sequences of transformations

Published online by Cambridge University Press:  19 September 2008

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
Copyright
Copyright © Cambridge University Press 1984

References

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