A monotone Sinai theorem
Dynamical Systems
2016-02-16 v3 Probability
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.
Cite
@article{arxiv.1311.6070,
title = {A monotone Sinai theorem},
author = {Anthony Quas and Terry Soo},
journal= {arXiv preprint arXiv:1311.6070},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/14-AOP968 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)