{
  "id": "1103.1063",
  "version": "v2",
  "published": "2011-03-05T15:46:10.000Z",
  "updated": "2011-09-27T15:59:49.000Z",
  "title": "Bernoulli actions are weakly contained in any free action",
  "authors": [
    "Miklós Abért",
    "Benjamin Weiss"
  ],
  "comment": "typos corrected",
  "categories": [
    "math.DS",
    "math.GR"
  ],
  "abstract": "We show that for any countable group, any free probability measure preserving action of the group weakly contains all Bernoulli actions of the group. It follows that for a finitely generated groups, the cost is maximal on Bernoulli actions and that all free factors of i.i.d.-s the group have the same cost. We also show that if a probability measure preserving action f is ergodic, but not strongly ergodic, then f is weakly equivalent to f\\timesI where I denotes the trivial action on the unit interval. This leads to a relative version of the Glasner-Weiss dichotomy.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-09-27T15:59:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22D40",
      "37B05",
      "37A15"
    ],
    "keywords": [
      "bernoulli actions",
      "free action",
      "free probability measure preserving action",
      "glasner-weiss dichotomy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.1063A"
    }
  }
}