{
  "abstract": "We establish an extension theorem for kappa-additive probability measures, where kappa is an arbitrary uncountable cardinal. Starting from a <kappa-algebra, we define an outer measure using coverings of cardinality at most kappa and characterise measurable sets by approximation in outer measure of symmetric differences. We prove that these sets form a kappa-algebra carrying a complete kappa-additive extension of the original measure. The extension is unique on the generated kappa-algebra, and its completion is the minimal domain admitting a complete kappa-additive extension. We also establish attainment of the covering infimum and show why the closure assumption on the initial algebra is essential. Examples include a strict extension of classical Lebesgue measure under the additional hypothesis add N = aleph_1 < cov N.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02729",
  "author_total": 1,
  "authors": [
    {
      "name": "Sviatoslav V. Dzhenzher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7fg8gw6wzr9c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02729",
  "fulltext_url": null,
  "id": "d7fg8gw6wzr9c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02729",
  "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.FA"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02729",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7fg8gw6wzr9c.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02729",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02729"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Extension of kappa-additive measures",
  "title_text": "Extension of kappa-additive measures",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/d7fg8gw6wzr9c",
  "venue": "arXiv",
  "versions": []
}