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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the clustering conjecture for Bernoulli factors of Bernoulli shifts


Author: G. Keller
Journal: Proc. Amer. Math. Soc. 111 (1991), 51-53
MSC: Primary 28D05; Secondary 54H20
MathSciNet review: 1034885
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Abstract: We give sufficient algebraic conditions on the probabilities $ {p_i}$ of a Bernoulli shift $ B({\mathbf{p}}){\text{ = }}B({p_1}, \ldots ,{p_M})$ which imply that if $ B({\mathbf{q}}) = B({q_1}, \ldots ,{q_N})$ is a continuous factor of $ B({\mathbf{p}})$, then $ {\mathbf{q}}$ is a clustering of $ {\mathbf{p}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1034885-X
PII: S 0002-9939(1991)1034885-X
Article copyright: © Copyright 1991 American Mathematical Society