{
  "abstract": "Wasserstein spaces carry two natural geometries: a vertical one, inherited from the linear structure of signed measures, and a horizontal one, induced by couplings. We prove that a Radon-Nikodym property holds in both. In the vertical geometry, bounded subsets of $P_p(R^d)$ are dentable in an ambient Banach space which itself fails the Radon-Nikodym property; we derive variational principles, Radon-Nikodym theorems for vector measures and martingale convergence results. In the horizontal geometry, we show that a Radon-Nikodym property is inherited from the one of spaces of random variables. We introduce horizontal martingales and prove that they are exactly the laws of $L^p$ -valued martingales.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12028",
  "author_total": 1,
  "authors": [
    {
      "name": "Charles Bertucci"
    }
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  "bibtex": "https://research.draconitic.com/paper/7wva5wetqw9hm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12028",
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  "id": "7wva5wetqw9hm",
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  "landing_url": "https://hal.science/hal-05737539v1",
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  "pdf_url": "https://hal.science/hal-05737539/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7wva5wetqw9hm.ris",
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    {
      "first_seen": "2026-10-30T12:17:27Z",
      "native_id": "hal-05737539",
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      "url": "https://hal.science/hal-05737539v1"
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      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12028"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Wasserstein spaces have the Radon-Nikodym property",
  "title_text": "Wasserstein spaces have the Radon-Nikodym property",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/7wva5wetqw9hm",
  "venue": "HAL",
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}