zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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
60J10Markov chains (discrete-time Markov processes on discrete state spaces)
28D05Measure-preserving transformations