{
  "id": "1510.04522",
  "version": "v1",
  "published": "2015-10-15T13:18:49.000Z",
  "updated": "2015-10-15T13:18:49.000Z",
  "title": "On functions of bounded variation",
  "authors": [
    "Christoph Aistleitner",
    "Florian Pausinger",
    "Anne Marie Svane",
    "Robert F. Tichy"
  ],
  "categories": [
    "math.CA",
    "math.FA",
    "math.NA"
  ],
  "abstract": "The recently introduced concept of $\\mathcal{D}$-variation unifies previous concepts of variation of multivariate functions. In this paper, we give an affirmative answer to the open question from Pausinger \\& Svane (J. Complexity, 2014) whether every function of bounded Hardy--Krause variation is Borel measurable and has bounded $\\mathcal{D}$-variation. Moreover, we show that the space of functions of bounded $\\mathcal{D}$-variation can be turned into a commutative Banach algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-15T13:18:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26B30",
      "65D30",
      "11K38"
    ],
    "keywords": [
      "bounded variation",
      "multivariate functions",
      "open question",
      "variation unifies",
      "bounded hardy-krause variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151004522A"
    }
  }
}