, Volume 40, Issue 3-4, pp 197-216

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.