{
  "id": "2003.01366",
  "version": "v1",
  "published": "2020-03-03T07:26:52.000Z",
  "updated": "2020-03-03T07:26:52.000Z",
  "title": "Ergodic Decomposition of Dirichlet Forms via Direct Integrals and Applications",
  "authors": [
    "Lorenzo Dello Schiavo"
  ],
  "comment": "35 pages",
  "categories": [
    "math.FA",
    "math.PR"
  ],
  "abstract": "We study superpositions and direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces, quasi-regular for the same underlying topology. The same holds for each quasi-regular strongly local Dirichlet space over a metrizable Luzin, Radon measure space, and admitting carr\\'e du champ operator. In this case, the representation is only projectively unique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-03T07:26:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "31C25",
      "60J25",
      "60J35"
    ],
    "keywords": [
      "direct integral",
      "dirichlet forms",
      "ergodic decomposition",
      "applications",
      "quasi-regular strongly local dirichlet space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}