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A skew-product which is Bernoulli

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Abstract

We show that if σ is the shift on sequences of {0,1} and τ is the entropy zero transformation used by Ornstein in constructing a counter-example toPinsker's conjecture, then the skew-product transformationT defined byT(x,y)=(σx,τx0 y) is Bernoulli. ThisT is conditionally mixing with respect to the independent generator for σ, a partition with full entropy.

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Authors and Affiliations

  1. Department of Mathematics, University of Toledo, 43606, Toledo, OH, USA

    Paul C. Shields

  2. Department of Mathematics, Stanford University, 94305, Stanford, CA, USA

    Robert Burton

Authors
  1. Paul C. Shields
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  2. Robert Burton
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Additional information

This research was done while the first author was a visitor at Stanford, supported in part by NSF Grant MP-575-08324.

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Shields, P.C., Burton, R. A skew-product which is Bernoulli. Monatshefte für Mathematik 86, 155–165 (1978). https://doi.org/10.1007/BF01320207

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  • DOI: https://doi.org/10.1007/BF01320207

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