{
  "id": "1511.05792",
  "version": "v1",
  "published": "2015-11-18T14:13:15.000Z",
  "updated": "2015-11-18T14:13:15.000Z",
  "title": "Ledrappier-Young formula and exact dimensionality of self-affine measures",
  "authors": [
    "Balázs Bárány",
    "Antti Käenmäki"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-18T14:13:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C45",
      "28A80"
    ],
    "keywords": [
      "exact dimensionality",
      "ledrappier-young formula",
      "long standing open problem",
      "quasi self-affine measures",
      "defining iterated function system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105792B"
    }
  }
}