{
  "id": "1008.1354",
  "version": "v2",
  "published": "2010-08-07T16:48:33.000Z",
  "updated": "2011-03-25T23:44:45.000Z",
  "title": "Sofic entropy and amenable groups",
  "authors": [
    "Lewis Bowen"
  ],
  "comment": "This new version corrects many errors from the previous version",
  "categories": [
    "math.DS"
  ],
  "abstract": "In previous work, I introduced a measure-conjugacy invariant for sofic group actions called sofic entropy. Here it is proven that the sofic entropy of an amenable group action equals its classical entropy. The proof uses a new measure-conjugacy invariant called upper-sofic entropy and a theorem of Rudolph and Weiss for the entropy of orbit-equivalent actions relative to the orbit change $\\sigma$-algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-25T23:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35"
    ],
    "keywords": [
      "measure-conjugacy invariant",
      "amenable group action equals",
      "sofic group actions",
      "upper-sofic entropy",
      "orbit-equivalent actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.1354B"
    }
  }
}