{
  "id": "1808.07661",
  "version": "v1",
  "published": "2018-08-23T08:21:04.000Z",
  "updated": "2018-08-23T08:21:04.000Z",
  "title": "Characterization of rectifiable measures in terms of $α$-numbers",
  "authors": [
    "Jonas Azzam",
    "Xavier Tolsa",
    "Tatiana Toro"
  ],
  "categories": [
    "math.CA",
    "math.AP",
    "math.MG"
  ],
  "abstract": "We characterize Radon measures $\\mu$ in $\\mathbb{R}^{n}$ that are $d$-rectifiable in the sense that their supports are covered up to $\\mu$-measure zero by countably many $d$-dimensional Lipschitz graphs and $\\mu \\ll \\mathcal{H}^{d}$. The characterization is in terms of a Jones function involving the so-called $\\alpha$-numbers. This answers a question left open in a former work by Azzam, David, and Toro.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-23T08:21:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "28A75",
      "28A78",
      "42B20"
    ],
    "keywords": [
      "rectifiable measures",
      "characterization",
      "dimensional lipschitz graphs",
      "question left open",
      "characterize radon measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}