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Induced Automorphisms and Related Concepts

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Part of the Texts and Readings in Mathematics book series (volume 6)

Abstract

Given a Borel automorphism σ on a Borel space (X, Ɓ) and a set A in Ɓ, the Poincaré recurrence lemma permits us to define (mod W σ ) a natural automorphism on A, where W σ denotes the σ ideal generated by the class of sets in Ɓ wandering under σ,(See Chapter 1). This map was given the name “induced transformation” (“induced automorphism”) by S. Kakutani who also studied its properties and used it to define a new kind of equivalence among the measure preserving automorphisms, now called Kakutani equivalence. In our exposition below of these concepts we will partly follow N. Friedman [2] who made these and related ideas available to a wider public.

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© Hindustan Book Agency 2013

Authors and Affiliations

  1. 1.University of MumbaiIndia

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