{
  "abstract": "We introduce the notions of $rgs$ and $irgs$ for Keisler measures, motivated by the study of generically stable random types and their associated Morley sequences. We obtain characterizations of these notions in terms of averages of classical first-order formulas over suitable probabilistic partitions (Theorems 3.2 and 3.3). We compare these notions with $fim$, $fam$, and self-averaging, and show that for types the notions $fim$, $irgs$, and $rgs$ coincide. We prove that if a definable global Keisler measure$μ$ is not dependent, then every Morley sequence in its canonical random extension $r_μ$ is divergent (Theorem 4.7). Consequently, every $irgs$ measure is dependent (Corollary 4.8) and hence symmetric (Corollary 4.13). Furthermore, we show that for $irgs$ measures the model-theoretic instability events $\\mathbf{O}^φ$, $\\mathbf{I}^φ$, and $\\mathbf{L}^φ$ have $\\mathbb{P}_μ$-measure zero (Theorem 5.4). In view of the equivalence of $fim$ and $irgs$ subsequently established in [6], this provides an alternative proof of the corresponding result for $fim$ measures in [9].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15870",
  "author_total": 1,
  "authors": [
    {
      "name": "Karim Khanaki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zveq2dnjs0p8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15870",
  "fulltext_url": null,
  "id": "9zveq2dnjs0p8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15870",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7161590571",
  "pdf_url": "https://arxiv.org/pdf/2605.15870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zveq2dnjs0p8.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2605.15870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Keisler Measures and Generically Stable Random Types",
  "title_text": "Keisler Measures and Generically Stable Random Types",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:42Z",
  "url": "https://research.draconitic.com/paper/9zveq2dnjs0p8",
  "venue": "arXiv",
  "versions": []
}