A monotone Sinai theorem

• Quas, Anthony ^[1] ; Soo, Terry ^[2]
  1. [1] University of Victoria

     University of Victoria

     Canadá

     
  2. [2] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 1, 2016, págs. 107-130
• Idioma: inglés
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• Resumen

  • 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.