A monotone isomorphism theorem
Dynamical Systems
2016-02-16 v2 Probability
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.
Cite
@article{arxiv.1509.01669,
title = {A monotone isomorphism theorem},
author = {Terry Soo},
journal= {arXiv preprint arXiv:1509.01669},
year = {2016}
}
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22 pages