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Finitary codings and weak Bernoulli partitions


Authors: A. del Junco and M. Rahe
Journal: Proc. Amer. Math. Soc. 75 (1979), 259-264
MSC: Primary 28D05
DOI: https://doi.org/10.1090/S0002-9939-1979-0532147-2
MathSciNet review: 532147
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Abstract: An example is constructed of a two state stationary stochastic process (T, P) whose time zero partition P is weak Bernoulli under the shift, but which cannot be the image under a finitary coding of any independent process. A sufficient condition for a partition to be weak Bernoulli is developed, based on the rate of convergence of the conditional entropy $ h(P\vert P_{ - j}^{ - 1})$ to $ h(P,T)$.


References [Enhancements On Off] (What's this?)

  • [1] M. A. Akcoglu, A. del Junco and M. Rahe, Finitary codes between Markov processes (preprint). MR 525312 (80d:28043)
  • [2] R. Bowen, Smooth partitions of Anosov diffeomorphisms are weak Bernoulli, Israel J. Math. 21 (1975), 95-100. MR 0385927 (52:6786)
  • [3] D. S. Ornstein, personal communication.
  • [4] M. Smorodinsky, A partition on a Bernoulli shift which is not weak Bernoulli, Math. Systems Theory 5 (1971), 201-203. MR 0297971 (45:7023)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0532147-2
Article copyright: © Copyright 1979 American Mathematical Society

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