{
  "id": "1708.01905",
  "version": "v1",
  "published": "2017-08-06T16:07:04.000Z",
  "updated": "2017-08-06T16:07:04.000Z",
  "title": "Sumsets contained in sets of upper Banach density 1",
  "authors": [
    "Melvyn B. Nathanson"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Every set $A$ of positive integers with upper Banach density 1 contains an infinite sequence of pairwise disjoint subsets $(B_i)_{i=1}^{\\infty}$ such that $B_i$ has upper Banach density 1 for all $i \\in \\mathbf{N}$ and $\\sum_{i\\in I} B_i \\subseteq A$ for every nonempty finite set $I$ of positive integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-06T16:07:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B05",
      "11B13",
      "11B75"
    ],
    "keywords": [
      "upper banach density",
      "positive integers",
      "nonempty finite set",
      "pairwise disjoint subsets",
      "infinite sequence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}