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The relative isomorphism theorem for Bernoulli flows

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Abstract

In this paper we extend the work of Thouvenot and others on Bernoulli splitting of ergodic transformations to ergodic flows of finite entropy. We prove that ifA is a factor of a flowS, whereS 1 is ergodic andA has a Bernoulli complement inS 1, thenA has a Bernoulli complement inS. Consequently, Bernoulli splitting for flows is stable under taking intermediate factors and certain\(\bar d\) limits. In addition it follows that the property of isomorphism with a Bernoulli × zero entropy flow is similarly stable.

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Authors and Affiliations

  1. Department of Mathematics, Wesleyan University, 06457, Middletown, CT, USA

    Adam Fieldsteel

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  1. Adam Fieldsteel
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Fieldsteel, A. The relative isomorphism theorem for Bernoulli flows. Israel J. Math. 40, 197–216 (1981). https://doi.org/10.1007/BF02761362

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  • DOI: https://doi.org/10.1007/BF02761362

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