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Skew products of Bernoulli shifts with rotations

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Abstracts

This paper investigates certain skew products of Bernoulli shifts with rotations or permutations, and shows that these transformations, if weak mixing, are also Bernoulli.

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References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Kakutani,Random ergodic theory and Markoff processes with a stable distribution, Proc. Second Berkeley Sympos. on Prob. and Stat., 1950, 247–261.

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

    Article  MATH  MathSciNet  Google Scholar 

  4. D. S. Ornstein,A Kolmogorov automorphism that is not a Bernoulli shift, to appear in Advances in Math.

  5. D. S. Ornstein,Imbedding Bernoulli shifts in flows, Lecture Notes in Math., Springer-Verlag, Berlin, 1970, 178–218. (Proc. of 1st Midwestern Conf. on Ergodic Theory, Ohio State Univ., March. 27–30, 1970.)

    Google Scholar 

  6. V. Rohlin,Fundamental ideas of measure theory, Mat. sb.25 (1949), 107–150 (in Russian) and Amer. Math. Soc. Transl., II Ser.,49 (1962), 1–54 (in English).

    MathSciNet  Google Scholar 

  7. J. G. Sinai,A weak isomorphism of transformations with an invariant measure, Dokl. Akad. Nauk SSSR147, (1962), 797–800 (in Russian) and Soviet Math. Dokl.3 (1962), 1725–1729 (in English).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. IBM, Yorktown Heights, New York

    R. L. Adler & P. C. Shields

  2. Stanford University, Stanford, California

    R. L. Adler & P. C. Shields

Authors
  1. R. L. Adler
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  2. P. C. Shields
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Additional information

This work was partially supported by the U. S. Air Force Office of Scientific Research under contract F44620-C-0063, P001, and by National Science Foundation under grant GP 21509.

This work was partially supportedby the National Science Foundation under grants GP 21509 and GJ-776.

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Adler, R.L., Shields, P.C. Skew products of Bernoulli shifts with rotations. Israel J. Math. 12, 215–222 (1972). https://doi.org/10.1007/BF02790748

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  • DOI: https://doi.org/10.1007/BF02790748

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