Abstract
In an attempt to further classifyK-automorphism D. Ornstein suggested (orally) a stronger mixing property calledweak Bernoulli (together with N. Friedman he proved that if a generator has this property then the transformation is isomorphic to a Bernoulli shift). I show that in a Bernoulli shift there is a partition which is not weak Bernoulli. I use the following theorem: The shift on a regular stationary Gaussian process is isomorphic to a Bernoulli shift.
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Research sponsored by the Air Force Office of Scientific Research, Office of Aerospace Research, United States Air Force, under Grant AF-AROSR-1312-67. Present address: Mathematics Institute, University of Warwick, Coventry CV4 7AL, England.
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Smorodinsky, M. A partition on a Bernoulli shift which is not weakly Bernoulli. Math. Systems Theory 5, 201–203 (1971). https://doi.org/10.1007/BF01694176
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DOI: https://doi.org/10.1007/BF01694176