Abstract
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.
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Acknowledgments
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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Dedicated to Professor Andrés del Junco, September 21, 1948 to June 17, 2015.
Funded in part by a New Faculty General Research Fund.
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Soo, T. A monotone isomorphism theorem. Probab. Theory Relat. Fields 167, 1117–1136 (2017). https://doi.org/10.1007/s00440-016-0700-x
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DOI: https://doi.org/10.1007/s00440-016-0700-x