{
  "id": "1308.6420",
  "version": "v2",
  "published": "2013-08-29T10:25:20.000Z",
  "updated": "2013-12-14T12:04:23.000Z",
  "title": "Avoiding σ-porous sets in Hilbert spaces",
  "authors": [
    "Michael Dymond"
  ],
  "categories": [
    "math.FA"
  ],
  "abstract": "We give a constructive proof that any $\\sigma$-porous subset of a Hilbert space has Lebesgue measure zero on typical $C^{1}$ curves. Further, we discover that this result does not extend to all forms of porosity; we find that even power-$p$ porous sets may meet many $C^{1}$ curves in positive measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-14T12:04:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hilbert space",
      "lebesgue measure zero",
      "porous subset",
      "constructive proof",
      "porous sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.6420D"
    }
  }
}