{
  "id": "2306.00768",
  "version": "v1",
  "published": "2023-06-01T15:03:35.000Z",
  "updated": "2023-06-01T15:03:35.000Z",
  "title": "Maps of bounded variation from PI spaces to metric spaces",
  "authors": [
    "Camillo Brena",
    "Francesco Nobili",
    "Enrico Pasqualetto"
  ],
  "comment": "38 pages",
  "categories": [
    "math.FA",
    "math.AP",
    "math.MG"
  ],
  "abstract": "We study maps of bounded variation defined on a metric measure space and valued into a metric space. Assuming the source space to satisfy a doubling and Poincar\\'e property, we produce a well-behaved relaxation theory via approximation by simple maps. Moreover, several equivalent characterizations are given, including a notion in weak duality with test plans.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-01T15:03:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "26A45",
      "26B30",
      "49J52",
      "30L99"
    ],
    "keywords": [
      "metric space",
      "bounded variation",
      "pi spaces",
      "metric measure space",
      "study maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}