{
  "id": "1612.06447",
  "version": "v1",
  "published": "2016-12-19T22:34:14.000Z",
  "updated": "2016-12-19T22:34:14.000Z",
  "title": "Strict and pointwise convergence of BV functions in metric spaces",
  "authors": [
    "Panu Lahti"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1612.06286",
  "categories": [
    "math.MG"
  ],
  "abstract": "In the setting of a metric space $X$ equipped with a doubling measure that supports a Poincar\\'e inequality, we show that if $u_i\\to u$ strictly in $BV(X)$, i.e. if $u_i\\to u$ in $L^1(X)$ and $\\Vert Du_i\\Vert(X)\\to\\Vert Du\\Vert(X)$, then for a subsequence (not relabeled) we have $\\widetilde{u}_i(x)\\to \\widetilde{u}(x)$ for $\\mathcal H$-almost every $x\\in X\\setminus S_u$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-19T22:34:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "30L99",
      "26B30",
      "28A20"
    ],
    "keywords": [
      "metric space",
      "bv functions",
      "pointwise convergence",
      "poincare inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}