{
  "id": "0705.2148",
  "version": "v5",
  "published": "2007-05-15T14:54:46.000Z",
  "updated": "2009-01-16T14:17:35.000Z",
  "title": "Predictability, entropy and information of infinite transformations",
  "authors": [
    "Jon Aaronson",
    "Kyewon Koh Park"
  ],
  "comment": "typos corrected, clarifications added, unproved result removed",
  "journal": "Fund. Math. 206 (2009), 1--21",
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We show that a certain type of quasi finite, conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic, measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole's transformation, information is asymptotically mod-normal with square root normalization. Lastly we see that certain ergodic, probability preserving transformations with zero entropy have analogous properties and consequently entropy dimension of at most 1/2.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2009-01-16T14:17:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A40",
      "60F05"
    ],
    "keywords": [
      "infinite transformations",
      "information",
      "measure preserving transformation",
      "quasi finite",
      "predictability"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0705.2148A"
    }
  }
}