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A monotone Sinai theorem

Quas, Anthony
; 
Soo, Terry
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Abstract
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.
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Date
2016-02-02
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Institute of Mathematical Statistics
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Mathematics Scholarly Works
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Soo_2016.pdf
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Keywords
Sinai factor theorem, Stochastic domination, Monotone coupling, Burton–Rothstein
Citation
Quas, Anthony; Soo, Terry. A monotone Sinai theorem. Ann. Probab. 44 (2016), no. 1, 107--130. doi:10.1214/14-AOP968. https://projecteuclid.org/euclid.aop/1454423036
URI
https://hdl.handle.net/1808/25521
DOI
10.1214/14-AOP968
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