{
  "id": "2401.15388",
  "version": "v1",
  "published": "2024-01-27T11:20:00.000Z",
  "updated": "2024-01-27T11:20:00.000Z",
  "title": "On sets where lip(f) is infinite for monotone continuous functions",
  "authors": [
    "Martin Rmoutil",
    "Thomas Zürcher"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Given an F-sigma-delta subset A of the real line R of Lebesgue measure zero, we construct a monotone absolutely continuous function f from R to R such that the little Lipschitz constant of f is equal to infinity exactly at points of A.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-27T11:20:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monotone continuous functions",
      "lebesgue measure zero",
      "little lipschitz constant",
      "monotone absolutely continuous function",
      "real line"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}