{
  "id": "1805.08279",
  "version": "v1",
  "published": "2018-05-21T20:15:00.000Z",
  "updated": "2018-05-21T20:15:00.000Z",
  "title": "Bernoulli shifts with bases of equal entropy are isomorphic",
  "authors": [
    "Brandon Seward"
  ],
  "categories": [
    "math.DS",
    "math.PR"
  ],
  "abstract": "We prove that if $G$ is a countably infinite group and $(L, \\lambda)$ and $(K, \\kappa)$ are probability spaces having equal Shannon entropy, then the Bernoulli shifts $G \\curvearrowright (L^G, \\lambda^G)$ and $G \\curvearrowright (K^G, \\kappa^G)$ are isomorphic. This extends Ornstein's famous isomorphism theorem to all countably infinite groups. Our proof builds on a slightly weaker theorem by Lewis Bowen in 2011 that required both $\\lambda$ and $\\kappa$ have at least $3$ points in their support. We furthermore produce finitary isomorphisms in the case where both $L$ and $K$ are finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-21T20:15:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A35"
    ],
    "keywords": [
      "bernoulli shifts",
      "equal entropy",
      "countably infinite group",
      "isomorphic",
      "extends ornsteins famous isomorphism theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}