A skew-product which is Bernoulli |
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Authors: | Paul C. Shields Robert Burton |
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Affiliation: | (1) Department of Mathematics, University of Toledo, 43606 Toledo, OH, USA;(2) Department of Mathematics, Stanford University, 94305 Stanford, CA, USA |
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Abstract: | We show that if is the shift on sequences of {0,1} and is the entropy zero transformation used by Ornstein in constructing a counter-example toPinsker's conjecture, then the skew-product transformationT defined byT(x,y)=(x,x0y) is Bernoulli. ThisT is conditionally mixing with respect to the independent generator for , a partition with full entropy.This research was done while the first author was a visitor at Stanford, supported in part by NSF Grant MP-575-08324. |
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