{
  "id": "2205.06864",
  "version": "v1",
  "published": "2022-05-13T19:42:37.000Z",
  "updated": "2022-05-13T19:42:37.000Z",
  "title": "Characterizing compact sets in $L^p$-spaces and its application",
  "authors": [
    "Katsuhisa Koshino"
  ],
  "categories": [
    "math.GN",
    "math.FA"
  ],
  "abstract": "In this paper, we give a characterization of compact sets in $L^p$-spaces on metric measure spaces, which is a generalization of the Kolmogorov-Riesz theorem. Using the criterion, we investigate the topological type of the space consisting of lipschitz maps with bounded supports.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-13T19:42:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54C35",
      "46B50",
      "46E30",
      "57N20"
    ],
    "keywords": [
      "characterizing compact sets",
      "application",
      "metric measure spaces",
      "kolmogorov-riesz theorem",
      "lipschitz maps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}