Quas, A;
Soo, T;
(2016)
A monotone Sinai theorem.
The Annals of Probability
, 44
(1)
pp. 107-130.
10.1214/14-aop968.
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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.
Type: | Article |
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Title: | A monotone Sinai theorem |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1214/14-aop968 |
Publisher version: | https://doi.org/10.1214/14-aop968 |
Language: | English |
Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
Keywords: | Sinai factor theorem, stochastic domination, monotone coupling, Burton–Rothstein. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
URI: | https://discovery.ucl.ac.uk/id/eprint/10089082 |
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