{
  "id": "2007.06326",
  "version": "v1",
  "published": "2020-07-13T11:45:59.000Z",
  "updated": "2020-07-13T11:45:59.000Z",
  "title": "Exact dimensionality and Ledrappier-Young formula for the Furstenberg measure",
  "authors": [
    "Ariel Rapaport"
  ],
  "comment": "43 pages",
  "categories": [
    "math.DS"
  ],
  "abstract": "Assuming strong irreducibility and proximality, we prove that the Furstenberg measure, corresponding to a finitely supported measure on the general linear group of a finite dimensional real vector space, is exact dimensional. We also establish a Ledrappier-Young type formula for its dimension. The general strategy of the proof is based on the argument given by Feng for the exact dimensionality of self-affine measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-13T11:45:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A80",
      "37C45"
    ],
    "keywords": [
      "exact dimensionality",
      "furstenberg measure",
      "ledrappier-young formula",
      "finite dimensional real vector space",
      "ledrappier-young type formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}