{
  "abstract": "We consider a capacity on a general measurable space associated with a sequence of identically distributed random variables. With a weak assumption concerned with the independence and very few restrictions on the capacity, we show that, on a set with full lower-capacity, any cluster point of empirical averages lies in the mean interval with the lower and upper Choquet integrals of the random variables being its bounds, and, under a Fubini-independent product capacity introduced by Ghirardato (1997), cluster points fill the whole mean interval with full upper-capacity. The results give answers to two open questions of Terán (2014).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27717",
  "author_total": 1,
  "authors": [
    {
      "name": "Li-Xin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f10zxpdb1rd6y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27717",
  "fulltext_url": null,
  "id": "f10zxpdb1rd6y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27717",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Fuzzy Systems and Optimization"
    ]
  ],
  "openalex": "W7223093649",
  "pdf_url": "https://arxiv.org/pdf/2610.27717",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f10zxpdb1rd6y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27717",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27717"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The law of large numbers for non-additive capacities without continuity",
  "title_text": "The law of large numbers for non-additive capacities without continuity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/f10zxpdb1rd6y",
  "venue": "arXiv",
  "versions": []
}