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Three bernoulli factors that generate an ergodic flow

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1342))

Abstract

We show that three Bernoulli invariant sub σ-algebras of an ergodic flow of positive entropy generate the full σ-algebra.

Research supported in part by NSF Grant DMS-8604202.

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References

  1. Abramov, L.M., On the entropy of a flow, Doklady Akad. Nank. SSSR 128, (1959), 873–875.

    MathSciNet  MATH  Google Scholar 

  2. Ambrose, W., Representation of ergodic flows, Ann of Math. 42, (1942), 723–739.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Ornstein, D.S., The isomorphism theorem for Bernoulli flow, Advances in Math. 10 (1973), 124–142.

    Article  MathSciNet  MATH  Google Scholar 

  5. Ornstein, D.S., Ergodic Theory, Randomness, and Dynamnical Systems. Yale University Press, 1974.

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  6. Park, K., Nice dense subset ergodic flows and Bernoulli flows. Pacific Journal of Mathematics, Vol. 119, No. 1, (1985), 181–190.

    Article  MathSciNet  MATH  Google Scholar 

  7. Park, K., Special family of ergodic flows and their d-limits, Israel J. of Math. Vol. 42, No. 4, (1982), 343–352.

    Article  MathSciNet  MATH  Google Scholar 

  8. Rudolph, D. J., A two-valued step coding for ergodic flows, Mathematische Zeitschrift (1976), 201–220.

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  9. Shields, P. The Theory of Bernoulli Shifts. Chicago University Press, Chicago, 1973.

    MATH  Google Scholar 

  10. Smorodinsky, M. and Thouvenot, J.P., Bernoulli factors that span a transformation, Israel J. of Math. Vol. 32, (1979), 39–43.

    Article  MathSciNet  MATH  Google Scholar 

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James C. Alexander

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© 1988 Springer-Verlag

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Park, K.K. (1988). Three bernoulli factors that generate an ergodic flow. In: Alexander, J.C. (eds) Dynamical Systems. Lecture Notes in Mathematics, vol 1342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082849

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  • DOI: https://doi.org/10.1007/BFb0082849

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50174-9

  • Online ISBN: 978-3-540-45946-0

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