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    A monotone Sinai theorem

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    Issue Date
    2016-02-02
    Author
    Quas, Anthony
    Soo, Terry
    Publisher
    Institute of Mathematical Statistics
    Type
    Article
    Article Version
    Scholarly/refereed, publisher version
    Metadata
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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.
    URI
    http://hdl.handle.net/1808/25521
    DOI
    https://doi.org/10.1214/14-AOP968
    Collections
    • Mathematics Scholarly Works [274]
    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

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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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