A non-Bernoulli skew product which is loosely Bernoulli |
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Authors: | Robert M Burton |
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Institution: | (1) Department of Mathematics, Oregon State University, 97330 Corvallis, OR, USA |
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Abstract: | LetT: Y→Y be the Bernoulli two shift with independent generatorQ={Q
0,Q
1} and letS: X→X be a measure preserving bijection. If (S, X) is ergodic then the skew product onX×Y defined by {fx339-1} is aK-automorphism. IfŜ is also Bernoulli we sayS is pre-Bernoulli. J. Feldman showed that ifS is pre-Bernoulli thenS must be loosely Bernoulli. We construct an example to show the converse is false, i.e. anS that is loosely Bernoulli but not pre-Bernoulli. |
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Keywords: | |
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