{
  "id": "1309.4945",
  "version": "v1",
  "published": "2013-09-19T11:57:27.000Z",
  "updated": "2013-09-19T11:57:27.000Z",
  "title": "Differentiation of sets - The general case",
  "authors": [
    "Estate V. Khmaladze",
    "Wolfgang Weil"
  ],
  "comment": "3 figures",
  "categories": [
    "math.CA",
    "math.DS"
  ],
  "abstract": "In recent work by Khmaladze and Weil (2008) and by Einmahl and Khmaladze (2011), limit theorems were established for local empirical processes near the boundary of compact convex sets $K$ in $\\R$. The limit processes were shown to live on the normal cylinder $\\Sigma$ of $K$, respectively on a class of set-valued derivatives in $\\Sigma$. The latter result was based on the concept of differentiation of sets at the boundary $\\partial K$ of $K$, which was developed in Khmaladze (2007). Here, we extend the theory of set-valued derivatives to boundaries $\\partial F$ of rather general closed sets $F\\subset \\R$, making use of a local Steiner formula for closed sets, established in Hug, Last and Weil (2004).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-19T11:57:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general case",
      "differentiation",
      "compact convex sets",
      "set-valued derivatives",
      "local steiner formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.4945K"
    }
  }
}