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Bernoulli shifts induced by K-automorphisms

✍ Scribed by Andrés Del Junco

Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
322 KB
Volume
25
Category
Article
ISSN
0001-8708

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✦ Synopsis

The purpose of this paper is to prove the following result. THEOREM 1. If u' is a Bernoulli shift with Jinite entropy on a probability space (Y', 9', v'), and E > 0 then there exists a probability space (X, F, CL) containing (Y', 9, v') (in the sense that Y' E 9, 9' = S Iy, = {FE 9 : F C Y'}, V' = ,.+,) such that /L(Y') > 1 -E, and a non-Bernoulli K-automorphism 7 of (X, 9, p) such that 7y' (the induced transformation of u' on Y') equals (J.

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Bernoulli shift is an invertible measure preserving transformation on the unit interval with Lebesgue measure that admits an independent generator, i.e., there exists a partition of the unit interval into a finite or countable number of disjoint sets of positive measure such that distinct iterates u