{
  "id": "1303.2368",
  "version": "v2",
  "published": "2013-03-10T19:40:13.000Z",
  "updated": "2013-03-14T06:57:57.000Z",
  "title": "An Arzelà-Ascoli theorem for the Hausdorff measure of noncompactness",
  "authors": [
    "Ben Berckmoes"
  ],
  "comment": "6 pages",
  "categories": [
    "math.FA"
  ],
  "abstract": "We generalize the Arzel\\`a-Ascoli theorem in the space of continuous maps on a compact interval with values in Euclidean N-space by providing a quantitative link between the Hausdorff measure of noncompactness in this space and a natural measure of non-uniform equicontinuity. The proof hinges upon a classical result of Jung's on the Chebyshev radius.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-14T06:57:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B50"
    ],
    "keywords": [
      "hausdorff measure",
      "arzelà-ascoli theorem",
      "noncompactness",
      "chebyshev radius",
      "euclidean n-space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}