{
  "id": "1912.04214",
  "version": "v1",
  "published": "2019-12-09T17:51:13.000Z",
  "updated": "2019-12-09T17:51:13.000Z",
  "title": "On Mazurkiewicz's sets, thin σ-ideals of compact sets and the space of probability measures on the rationals",
  "authors": [
    "Roman Pol",
    "Piotr Zakrzewski"
  ],
  "categories": [
    "math.GN"
  ],
  "abstract": "We shall establish some properties of thin $\\sigma$-ideals of compact sets in compact metric spaces (in particular, the $\\sigma$-ideals of compact null-sets for thin subadditive capacities), and we shall refine the celebrated theorem of David Preiss that there exist compact non-uniformly tight sets of probability measures on the rationals. Both topics will be based on a construction of Stefan Mazurkiewicz from his 1927 paper containing a solution of a Urysohn's problem in dimension theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-09T17:51:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "54H05",
      "28A33",
      "28A12"
    ],
    "keywords": [
      "compact sets",
      "probability measures",
      "mazurkiewiczs sets",
      "compact metric spaces",
      "compact non-uniformly tight sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}