{
  "id": "1311.6070",
  "version": "v2",
  "published": "2013-11-24T00:09:50.000Z",
  "updated": "2014-09-03T02:22:23.000Z",
  "title": "A monotone Sinai theorem",
  "authors": [
    "Anthony Quas",
    "Terry Soo"
  ],
  "comment": "26 pages",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "Sinai proved that a non-atomic 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-24T00:09:50.000Z",
      "abstract": "Sinai proved that a non-atomic 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 zeroth coordinate of the resulting Bernoulli process is no greater than that of the zeroth coordinate of the original process.",
      "comment": "24 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-03T02:22:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35",
      "60G10",
      "60E15"
    ],
    "keywords": [
      "monotone sinai theorem",
      "bernoulli shift",
      "factor map",
      "non-atomic ergodic measure-preserving system",
      "monotone factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.6070Q"
    }
  }
}