{
  "id": "2005.06309",
  "version": "v1",
  "published": "2020-05-13T13:31:41.000Z",
  "updated": "2020-05-13T13:31:41.000Z",
  "title": "Nonsingular Bernoulli actions of arbitrary Krieger type",
  "authors": [
    "Tey Berendschot",
    "Stefaan Vaes"
  ],
  "categories": [
    "math.DS",
    "math.GR",
    "math.OA"
  ],
  "abstract": "We prove that every infinite amenable group admits Bernoulli actions of any possible Krieger type, including type $II_\\infty$ and type $III_0$. We obtain this result as a consequence of general results on the ergodicity and Krieger type of nonsingular Bernoulli actions $G \\curvearrowright \\prod_{g \\in G} (X_0,\\mu_g)$ with arbitrary base space $X_0$, both for amenable and for nonamenable groups. Earlier work focused on two point base spaces $X_0 = \\{0,1\\}$, where type II$_\\infty$ was proven not to occur.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-13T13:31:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonsingular bernoulli actions",
      "arbitrary krieger type",
      "amenable group admits bernoulli actions",
      "infinite amenable group admits bernoulli",
      "base space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}