Skip to main content
SpringerLink
Log in

On induced transformations of Bernoulli shifts

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. L. Abramov, The entropy of a derived automorphism,Amer. Math. Soc. Translations, Series 2, Vol. 49, pp. 162–166.

  2. V. Arnold andA. Avez,Ergodic Problems of Classical Mechanics, Benjamin, New York, 1968.

    Google Scholar 

  3. P. Billingsley,Ergodic Theory and Information, John Wiley and Sons, New York, 1965.

    Google Scholar 

  4. R. V. Chacon, Change of velocity of flows,J. Math. Mech. 16 (1966), 417–431.

    Google Scholar 

  5. N. A. Friedman,Introduction to Ergodic Theory, Van Nostrand, Princeton, 1970.

    Google Scholar 

  6. N. A. Friedman andD. Ornstein, On induced transformations, Tech. Report, University of New Mexico.

  7. N. A. Friedman andD. Ornstein, On isomorphism of weak Bernoulli transformations,Advances in Math. 5 (1970), 365–394.

    Google Scholar 

  8. S. Kakutani, Induced measure-preserving transformations,Proc. Imp. Acad. Tokyo 19 (1943), 635–641.

    Google Scholar 

  9. D. Ornstein, Bernoulli shifts with the same entropy are isomorphic,Advances in Math. 4 (1970), 337–352.

    Google Scholar 

  10. D. Ornstein, Two Bernoulli shifts with infinite entropy are isomorphic,Advances in Math. 5 (1970), 339–348.

    Google Scholar 

  11. W. Parry,Entropy and Generators in Ergodic Theory, Benjamin, New York, 1969.

    Google Scholar 

  12. V. Rohlin, On the fundamental ideas of measure theory,Mat. Sb. 67 (1949), 107–150. [Amer. Math. Soc. Transl. No. 71 (1952).]

    Google Scholar 

  13. V. Rohlin, Lectures on the entropy theory of measure-preserving transformations,Russian Math. Surveys (5)22 (1967), 1–52.

    Google Scholar 

  14. M. Smorodinsky, An exposition of Ornstein's isomorphism theorem for Bernoulli shifts,Advances in Math. (to appear).

  15. M. Smorodinsky, A Bernoulli partition which is not weakly Bernoulli,Math. Systems Theory 5 (1971), 201–203.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Virginia, 22903, Charlottesville, Virginia, USA

    Alan Saleski

Authors
  1. Alan Saleski
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

These results are contained in the author's doctoral dissertation written at the University of California at Berkeley under the guidance of Professor Jacob Feldman to whom the author is very grateful for both encouragement and advice. In addition, the author wishes to thank Professor William Parry for several helpful suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saleski, A. On induced transformations of Bernoulli shifts. Math. Systems Theory 7, 83–96 (1973). https://doi.org/10.1007/BF01824810

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01824810

Keywords

Search

Navigation