{
  "id": "1808.09711",
  "version": "v1",
  "published": "2018-08-29T10:04:36.000Z",
  "updated": "2018-08-29T10:04:36.000Z",
  "title": "Fine properties of functions with bounded variation in Carnot-Carathéodory spaces",
  "authors": [
    "Sebastiano Don",
    "Davide Vittone"
  ],
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We study properties of functions with bounded variation in Carnot-Ca\\-ra\\-th\\'eo\\-do\\-ry spaces. We prove their almost everywhere approximate differentiability and we examine their approximate discontinuity set and the decomposition of their distributional derivatives. Under an additional assumption on the space, called property $\\mathcal R$, we show that almost all approximate discontinuities are of jump type and we study a representation formula for the jump part of the derivative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T10:04:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "53C17",
      "49Q15",
      "28A75"
    ],
    "keywords": [
      "bounded variation",
      "carnot-carathéodory spaces",
      "fine properties",
      "approximate discontinuity set",
      "study properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}