A classification of the finite extensions of a multidimensional Bernoulli shift

Kammeyer, Janet Whalen

doi:10.1090/S0002-9947-1993-1076616-X

A classification of the finite extensions of a multidimensional Bernoulli shift
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Trans. Amer. Math. Soc. 335 (1993), 443-457 Request permission

Abstract:

The finite extensions of a multidimensional Bernoulli shift are classified completely, up to factor isomorphism, and up to isomorphism. If such an extension is weakly mixing then it must be Bernoulli; otherwise, it has a finite rotation factor, which has a Bernoulli complementary algebra. This result is extended to multidimensional Bernoulli flows and Bernoulli shifts of infinite entropy.

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