{
  "id": "0706.4343",
  "version": "v1",
  "published": "2007-06-29T01:44:49.000Z",
  "updated": "2007-06-29T01:44:49.000Z",
  "title": "Hausdorff Dimension and Hausdorff Measure for Non-integer based Cantor-type Sets",
  "authors": [
    "Qinghe Yin"
  ],
  "categories": [
    "math.DS",
    "math.MG"
  ],
  "abstract": "We consider digits-deleted sets or Cantor-type sets with $\\beta$-expansions. We calculate the Hausdorff dimension $d$ of these sets and show that $d$ is continuous with respect to $\\beta$. The $d$-dimentional Hausdorff measure of these sets is finite and positive.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-06-29T01:44:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hausdorff dimension",
      "cantor-type sets",
      "non-integer",
      "dimentional hausdorff measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.4343Y"
    }
  }
}