{
  "abstract": "A submetric space is a topological space equipped with a continuous metric that generates a metric topology (usually) weaker than the original one (e.g., a~separable Hilbert space with the weak topology). We show that a positive linear functional on the space of bounded continuous functions on a submetric space is given as an integral with respect to a tight measure if, and only if, it is continuous in the strict topology. Neither local compactness nor complete regularity is required. We link the equicontinuity of a family of functionals in the strict topology to the uniform tightness of the underlying measures, and we provide a probabilistic representation (Skorokhod's parametrization) for such families. Finally, we identify the finest topology on the space of probability measures on a submetric space in which uniform tightness implies relative compactness. In non-metric spaces this topology is strictly stronger than the topology of weak convergence of probability measures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35661",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Jakubowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f3n1cksexgbdm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35661",
  "fulltext_url": null,
  "id": "f3n1cksexgbdm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35661",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7223816810",
  "pdf_url": "https://arxiv.org/pdf/2610.35661",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f3n1cksexgbdm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35661",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35661"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Riesz representation in submetric spaces and its probabilistic aspects",
  "title_text": "The Riesz representation in submetric spaces and its probabilistic aspects",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/f3n1cksexgbdm",
  "venue": "arXiv",
  "versions": []
}