{
  "id": "0803.3525",
  "version": "v3",
  "published": "2008-03-25T11:03:42.000Z",
  "updated": "2008-04-26T08:16:29.000Z",
  "title": "On the size of Nikodym sets in finite fields",
  "authors": [
    "Liangpan Li"
  ],
  "comment": "4 pages",
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $\\mathbb{F}_q$ denote a finite field of $q$ elements. Define a set $B\\subset\\mathbb{F}_q^n$ to be Nikodym if for each $x\\in B^{c}$, there exists a line $L$ such that $L\\cap B^c=\\{x\\}.$ The main purpose of this note is to show that the size of every Nikodym set is at least $C_n\\cdot q^n$, where $C_n$ depends only on $n$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-04-26T08:16:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11T99"
    ],
    "keywords": [
      "nikodym set",
      "finite field",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.3525L"
    }
  }
}