{
  "id": "1612.06286",
  "version": "v1",
  "published": "2016-12-19T17:40:07.000Z",
  "updated": "2016-12-19T17:40:07.000Z",
  "title": "A Federer-style characterization of sets of finite perimeter on metric spaces",
  "authors": [
    "Panu Lahti"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "In the setting of a metric space equipped with a doubling measure that supports a Poincar\\'e inequality, we show that a set $E$ is of finite perimeter if and only if $\\mathcal H(\\partial^1 I_E)<\\infty$, that is, if and only if the codimension one Hausdorff measure of the \\emph{$1$-fine boundary} of the set's measure theoretic interior $I_E$ is finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T17:40:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30L99",
      "31E05",
      "26B30"
    ],
    "keywords": [
      "finite perimeter",
      "metric space",
      "federer-style characterization",
      "sets measure theoretic interior",
      "fine boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}