{
  "id": "1904.10031",
  "version": "v1",
  "published": "2019-04-22T18:55:34.000Z",
  "updated": "2019-04-22T18:55:34.000Z",
  "title": "A combinatorial proof of the pointwise ergodic theorem for actions of amenable groups along Tempelman Følner Sequences",
  "authors": [
    "Jonathan Boretsky",
    "Jenna Zomback"
  ],
  "comment": "5 pages",
  "categories": [
    "math.DS",
    "math.LO"
  ],
  "abstract": "We generalize A. Tserunyan's proof of the pointwise ergodic theorem for $\\mathbb{Z}$ to give a short and combinatorial proof of the pointwise ergodic theorem for actions of amenable groups along Tempelman F{\\o}lner sequences. We do this by finding Vitali coverings with F{\\o}lner tiles in multiple scales.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-22T18:55:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A30",
      "03E15"
    ],
    "keywords": [
      "pointwise ergodic theorem",
      "tempelman følner sequences",
      "combinatorial proof",
      "amenable groups",
      "tserunyans proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}