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Israel Journal of Mathematics

, Volume 21, Issue 2–3, pp 215–232 | Cite as

Remarques sur les systemes dynamiques donnes avec plusieurs facteurs

  • Jean-Paul Thouvenot
Article

Abstract

Two Bernoulli shifts are given, (X, T) and (X′, T′), with independent generatorsR=PQ andR′=P′ ∨Q′ respectively. (R andR′ are finite). One can chooseR such that if (X′, T′) can be made a factor of (X, T) in such a way that (P′) T′ and (Q′) T′ are full entropy factors of (P) T and (Q) T respectively thend (PQ)=d(P′Q′). In addition it is proved that if (X, T) is a Bernoulli shift and ifS is a measure preserving transformation ofX that has the same factor algebras asT thenS=T orS=T −1. A tool for this proof, which may be of independent interest is a relative version for very weak Bernoullicity.

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Bibliographie

  1. 1.
    R. L. Adler,Ergodic and mixing properties of infinite memory channels, Proc. Amer. Math. Soc.12 (1961), 924–930.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    D. L. Burkholder et Y. S. Chow,Iterates of conditional expectation operators, Proc. Amer. Math. Soc.,12 (1961), 490–495.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    D. S. Ornstein,Imbedding Bernoulli shifts in flows, Contribution to ergodic theory and Probability, Lectures notes in Mathematics Series, Springer-Verlag Berlin, 1970, pp. 178–218.Google Scholar
  4. 4.
    D. S. Ornstein,A mixing transformation that commutes only with its powers, Proc. Sixth Berkeley Symp. Math. Stat. Prob. University of California Press, 1967, vol. II, part 2, pp. 335–360.Google Scholar
  5. 5.
    P. C. Shields,Bernoulli shifts are determined by their factor algebras, Proc. Amer. Math. Soc.,41 (1973), 331–332.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    J. P. Thouvenot,Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l’un est un schéma de Bernoulli, Israel J. Math.21 (1975), 177–207.MATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1975

Authors and Affiliations

  • Jean-Paul Thouvenot
    • 1
  1. 1.Laboratoire de ProbabilitésUniversité de Paris VI - Tour 56Paris Cedex 05France

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