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Classification of ergodic finitary shifts. (English) Zbl 0565.60059

From the authors’ introduction: R. L. Adler, P. Shields and the reviewer [Ann. Math. Stat. 43, 1027-1029 (1972; Zbl 0244.60053)] have shown that every irreducible finite state Markov shift is isomorphic to a direct product of a rotation and a Bernoulli shift.

In this paper this result is extend to a wider class of shifts, the so called finitary shifts. These shifts are induced by finitary processes defined by A. Heller [ibid. 36, 1286-1291 (1965; Zbl 0139.346)]. He proved that these processes include Markov chains and also functionals of Markov chains and gave an example of a process which is finitary and is not a functional of a Markov chain.

Reviewer: M.Smorodinsky
MSC:
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
28D05Measure-preserving transformations