{
  "abstract": "Given a first-order theory $T$ (in discrete or continuous logic) and a Borel-definable global Keisler measure $μ$ in $T$, we show that the following conditions are equivalent: $(i)$ $μ$ is a frequency interpretation measure; $(ii)$ $μ$ is definable and its canonical \"random extension\" $r_μ$ is generically stable in the randomization theory $T^R$; $(iii)$ $μ$ is \"self-averaging\". This result establishes a robust notion of generic stability for Keisler measures, which resolves a long-term research objective from previous work. The implications $(i)\\Rightarrow(ii)\\Rightarrow (iii)$ were previously established by the authors (for $T$ discrete). The primary focus of this paper is the reverse implications $(iii)\\Rightarrow (ii)\\Rightarrow(i)$. We also prove that generically stable measures are closed under Morley products, answering another well-known question that was open even in the case of types. These results are obtained through the use of AI models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.24605",
  "author_total": 3,
  "authors": [
    {
      "name": "Gabriel Conant"
    },
    {
      "name": "Kyle Gannon"
    },
    {
      "name": "James E. Hanson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eh78wmtnhzdpq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.24605",
  "fulltext_url": null,
  "id": "eh78wmtnhzdpq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.24605",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7204267153",
  "pdf_url": "https://arxiv.org/pdf/2608.24605",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eh78wmtnhzdpq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2608.24605",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.24605"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Generically stable Keisler measures",
  "title_text": "Generically stable Keisler measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/eh78wmtnhzdpq",
  "venue": "arXiv",
  "versions": []
}