{
  "abstract": "We study linear delay differential equations whose delay terms are represented by time-dependent finite signed measures. This framework accommodates discrete, distributed, and singular delay contributions without requiring continuity of the coefficient paths in time. We establish well-posedness in the Carathéodory sense and sequential dependence of solutions on the measure-valued parameters under almost-everywhere weak-* convergence and a common total variation bound. A central part of the analysis associates a signed measure on the time--delay domain with each coefficient path and establishes an equivalent integral formulation. This representation yields three equivalent characterizations of a $σ$-algebra on the parameter space suited to measurability of the continuation operator. A measurable fixed-point argument then provides measurability of the solution maps, despite the possible failure of continuity in the product weak-* topology. For coefficients generated by a measure-preserving base flow, these results lead to measurable linear skew-product semiflows on continuous and absolutely continuous phase spaces. Under additional ergodic hypotheses and the assumption of a finite top Lyapunov exponent, eventual compactness and regularization yield Oseledets decompositions with the same Lyapunov exponents and multiplicities on both spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21098",
  "author_total": 1,
  "authors": [
    {
      "name": "Marek Kryspin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k4j1v363adbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21098",
  "fulltext_url": null,
  "id": "6k4j1v363adbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21098",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Mathematical Dynamics and Fractals"
    ]
  ],
  "openalex": "W7213928435",
  "pdf_url": "https://arxiv.org/pdf/2609.21098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k4j1v363adbr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Delay equations with measure-valued coefficients: From Carathéodory solutions to measurable semiflows",
  "title_text": "Delay equations with measure-valued coefficients: From Carathéodory solutions to measurable semiflows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/6k4j1v363adbr",
  "venue": "arXiv",
  "versions": []
}