Probability Theory and Related Fields

, Volume 167, Issue 3–4, pp 1117–1136 | Cite as

A monotone isomorphism theorem

  • Terry SooEmail author


In the simple case of a Bernoulli shift on two symbols, zero and one, by permuting the symbols, it is obvious that any two equal entropy shifts are isomorphic. We show that the isomorphism can be realized by a factor that maps a binary sequence to another that is coordinatewise smaller than or equal to the original sequence.


Sinai factor theorem Ornstein theorem Stochastic domination Monotone coupling Burton–Rothstein 

Mathematics Subject Classification

37A35 60G10 60E15 



I thank Zemer Kosloff for his help with Example 1. I also thank the referee for the careful reading of this paper and useful suggestions.


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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