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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
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)$.


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