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January 2016 A monotone Sinai theorem
Anthony Quas, Terry Soo
Ann. Probab. 44(1): 107-130 (January 2016). DOI: 10.1214/14-AOP968

Abstract

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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Anthony Quas. Terry Soo. "A monotone Sinai theorem." Ann. Probab. 44 (1) 107 - 130, January 2016. https://doi.org/10.1214/14-AOP968

Information

Received: 1 November 2013; Revised: 1 September 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1359.37014
MathSciNet: MR3456333
Digital Object Identifier: 10.1214/14-AOP968

Subjects:
Primary: 37A35, 60E15, 60G10

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 1 • January 2016
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