Induced Automorphisms and Related Concepts
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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  who made these and related ideas available to a wider public.
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