A monotone Sinai theorem

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Issue Date
2016-02-02Author
Quas, Anthony
Soo, Terry
Publisher
Institute of Mathematical Statistics
Type
Article
Article Version
Scholarly/refereed, publisher version
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Show full item recordAbstract
Sinai proved that a nonatomic ergodic measure-preserving system has any Bernoulli shift of no greater entropy as a factor. Given a Bernoulli shift, we show that any other Bernoulli shift that is of strictly less entropy and is stochastically dominated by the original measure can be obtained as a monotone factor; that is, the factor map has the property that for each point in the domain, its image under the factor map is coordinatewise smaller than or equal to the original point.
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Citation
Quas, Anthony; Soo, Terry. A monotone Sinai theorem. Ann. Probab. 44 (2016), no. 1, 107--130. doi:10.1214/14-AOP968. https://projecteuclid.org/euclid.aop/1454423036
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