{
  "abstract": "V. Fedorchuk, A. Chizogidze, and T. Banakh in 2003 and V. Bogachev in 2024 posed the following questions: (i) is it true that $P_τ(X)$ is $C$-embedded in $P_σ(X)$; (ii) Is it true that $P_R(X)$ is $C$-embedded in $P_R(βX)$ if and only if $X$ is pseudocompact, where $P_σ$, $P_τ$, and $P_R$ are the functors of probability $σ$-additive on the Baire $σ$-algebra, $τ$-additive, and Radon measures on the space $X$? The answers to these questions are negative. However, if instead of probability measures we consider the corresponding alternating measures $M_σ$, $M_τ$, and $M_R$, the situation changes. It is proved that (i) $M_τ(X)$ is $C$-embedded in $M_σ(X)$; (ii) $M_R(X)$ is $C$-embedded in $M_R(βX)$ if and only if $X$ is pseudocompact. The question of $C$-embedding of measure spaces is an extension of the question of coincidence of measure spaces, which is a development of the classical concepts of universally measurable and universal measure zero sets. A general theorem is obtained, which leads to the mentioned results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: E. A. Reznichenko and Yu V. Sadovnichiy. A new approach to universal measurement. Bulletin of the Institute of Mathematics of the National Academy of Sciences of the Kyrgyz Republic, (2):2, 2025",
  "arxiv": "2609.14414",
  "author_total": 2,
  "authors": [
    {
      "name": "Reznichenko E. A."
    },
    {
      "name": "Sadovnichiy Yu. V"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahw6svecmvn40.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14414",
  "fulltext_url": null,
  "id": "ahw6svecmvn40",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14414",
  "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.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.PR"
    ],
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      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7213313655",
  "pdf_url": "https://arxiv.org/pdf/2609.14414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahw6svecmvn40.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14414"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A New Approach to Universal Measurability",
  "title_text": "A New Approach to Universal Measurability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/ahw6svecmvn40",
  "venue": "arXiv",
  "versions": []
}