{
  "id": "2107.02699",
  "version": "v1",
  "published": "2021-07-06T16:01:52.000Z",
  "updated": "2021-07-06T16:01:52.000Z",
  "title": "On normal numbers and self-similar measures",
  "authors": [
    "Simon Baker"
  ],
  "categories": [
    "math.DS",
    "math.CA",
    "math.NT"
  ],
  "abstract": "In this paper we prove that if $\\{\\varphi_i(x)=\\lambda x+t_i\\}$ is an equicontractive iterated function system and $b$ is a positive integer satisfying $\\frac{\\log b}{\\log |\\lambda|}\\notin\\mathbb{Q},$ then almost every $x$ is normal in base $b$ for any non-atomic self-similar measure of $\\{\\varphi_i\\}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-06T16:01:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "normal numbers",
      "non-atomic self-similar measure",
      "equicontractive iterated function system",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}