A MONOTONE SINAI THEOREM

• 成果类型: Article
• 署名作者: Quas, Anthony; Soo, Terry
• 署名单位: University of Victoria; University of Kansas
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP968
• 发表日期: 2016
• 页码: 107-130
• 关键词: isomorphism-problem; bernoulli-shifts; finitary codes; entropy

摘要

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.