Advertisement

Israel Journal of Mathematics

, Volume 21, Issue 2–3, pp 145–153 | Cite as

Factors of Bernoulli shifts

  • Donald S. Ornstein
Article

Abstract

An example is constructed of a proper factor of a Bernoulli shift, that cannot be increased without increasing its entropy, and still has no independent complement. The construction mirrors, in a sense, that of aK-automorphism that is not a Bernoulli shift.

Keywords

Invariant Measure Ergodic Theorem Bernoulli Shift Conditional Measure Isomorphism Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Ornstein,Ergodic Theory, Randomness, and Dynamical Systems, Yale U. Press, 1974.Google Scholar
  2. 2.
    J.-P. Thouvenot,Quelques propriétés des systèmes dynamiques qui se décomposent en un produit de deux systèmes dont l’un est un schema de Bernoulli. Israel J. Math.21 (1975), 177–207.MATHMathSciNetGoogle Scholar
  3. 3.
    J.-P. Thouvenot,Une classe de systèmes pour lesquels la conjecture de Pinsker est vraie, Israel J. Math.21 (1975), 208–214.MATHMathSciNetGoogle Scholar
  4. 4.
    J.-P. Thouvenot and P. C. Shields,Entropy zero × Bernoulli processes are closed in the \(\bar d\), to appear.Google Scholar
  5. 5.
    D. S. Ornstein and B. Weiss,Finitely determined implies very weak Bernoulli, Israel J. Math.17 (1974), 94–104.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    K. Berg,Convolution of invariant measures, maximal entropy, Math. Systems Theory3 (1969), 146–151.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1975

Authors and Affiliations

  • Donald S. Ornstein
    • 1
  1. 1.Stanford UniversityStanfordU.S.A.

Personalised recommendations