The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 107-130.
A monotone Sinai theorem
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.
Ann. Probab., Volume 44, Number 1 (2016), 107-130.
Received: November 2013
Revised: September 2014
First available in Project Euclid: 2 February 2016
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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