{
  "id": "2209.07968",
  "version": "v1",
  "published": "2022-09-16T14:35:08.000Z",
  "updated": "2022-09-16T14:35:08.000Z",
  "title": "On Mukhin's necessary and sufficient condition for the validity of the local limit theorem",
  "authors": [
    "Michel J. G. Weber"
  ],
  "comment": "4 pages. arXiv admin note: substantial text overlap with arXiv:2208.02700",
  "categories": [
    "math.PR"
  ],
  "abstract": "Mukhin found in 1984 an important necessary and sufficient condition for the validity of the local limit theorem. Revisiting the succint proof given in \\cite{Mu2}, we could only prove rigorously a weaker necessary and sufficient condition, with a significantly different formulation. This is the object of this short Note.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-16T14:35:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F15",
      "60G50",
      "60F05"
    ],
    "keywords": [
      "local limit theorem",
      "sufficient condition",
      "mukhins necessary",
      "weaker necessary",
      "succint proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}