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


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.


Download Citation

Anthony Quas. Terry Soo. "A monotone Sinai theorem." Ann. Probab. 44 (1) 107 - 130, January 2016.


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

Primary: 37A35 , 60E15 , 60G10

Keywords: Burton–Rothstein , monotone coupling , Sinai factor theorem , stochastic domination

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
Back to Top