{
  "id": "1807.05905",
  "version": "v1",
  "published": "2018-07-16T15:00:57.000Z",
  "updated": "2018-07-16T15:00:57.000Z",
  "title": "Weak mixing for nonsingular Bernoulli actions of countable groups",
  "authors": [
    "Alexandre I. Danilenko"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $A$ be a finite set, $G$ a discrete countable infinite group and $(\\mu_g)_{g\\in G}$ a family of probability measures on $A$ such that $\\inf_{g\\in G}\\min_{a\\in A}\\mu_g(a)>0$. It is shown (among other results) that if the Bernoulli shiftwise action of $G$ on the infinite product space $\\bigotimes_{g\\in G}(A,\\mu_g)$ is nonsingular and conservative then it is weakly mixing. This answers in positive a question by Z.~Kosloff who proved recently a weaker version of this result for $G=\\Bbb Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-16T15:00:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A40",
      "37A20"
    ],
    "keywords": [
      "nonsingular bernoulli actions",
      "countable groups",
      "weak mixing",
      "discrete countable infinite group",
      "infinite product space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}