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A complete classification of the two-point extensions of a multidimensional bernoulli shift

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Abstract

A theorem is proven which gives five characterizations of a multidimensional Bernoulli shift. The two-point extensions of a multidimensional Bernoulli shift are classified completely. If such an extension is weakly mixing then it must be Bernoulli; otherwise, it is isomorphic to one of 2n specific trivial extensions. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy.

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Authors and Affiliations

  1. Department of Mathematics, United States Naval Academy, 21402, Annapolis, MD, USA

    Janet Whalen Kammeyer

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  1. Janet Whalen Kammeyer
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Additional information

This work supported in part by N.S.F. Grant DMS-85-04701 and by the University of Maryland Department of Mathematics.

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Kammeyer, J.W. A complete classification of the two-point extensions of a multidimensional bernoulli shift. J. Anal. Math. 54, 113–163 (1990). https://doi.org/10.1007/BF02796146

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  • DOI: https://doi.org/10.1007/BF02796146

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