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Wasserstein spaces have the Radon-Nikodym property — arXiv:2609.12028

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.12028
License (as archived): CC0-1.0
Archived: 2026-10-16T03:44:27.336Z
SHA-256 of the archived text: d73470d656c7344d93f1489a2195348a8b216f8517444c31a2372a16bbbb8c2c
Stable URL of this page: https://metraipolis.com/documento/dc_f0732cdad201

How to cite

Wasserstein spaces have the Radon-Nikodym property — arXiv:2609.12028 — arXiv (en), https://arxiv.org/abs/2609.12028 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_f0732cdad201 (Metraipolis archive dc_f0732cdad201, sha256 d73470d656c7344d93f1489a2195348a8b216f8517444c31a2372a16bbbb8c2c)

BibTeX

@misc{dcf0732cdad201,
  title = {Wasserstein spaces have the Radon-Nikodym property — arXiv:2609.12028},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.12028},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_f0732cdad201; sha256 d73470d656c7344d93f1489a2195348a8b216f8517444c31a2372a16bbbb8c2c},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.12028. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-14 in math.OC).
Categorie arXiv: Functional Analysis (math.FA) ; Optimization and Control (math.OC); Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2609.12028 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-16T03:15:38.823Z dalla pagina https://arxiv.org/catchup/math.OC/2026-09-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).