Probability measure annihilating all finite-dimensional subspaces

[2512.21664] Probability measure annihilating all finite-dimensional subspaces Skip to main content Search Submit Donate Log in Mathematics > Functional Analysis arXiv:2512.21664 (math) [Submitted on 25 Dec 2025 ( v1 ), last revised 24 Aug 2026 (this version, v4)] Title: Probability measure annihilating all finite-dimensional subspaces Authors: Nizar El Idrissi , Hicham Zoubeir View PDF HTML (experimental) Abstract: We propose in this short note a prime numbers-based method for constructing probability measures on infinite-dimensional Banach spaces annihilating all finite-dimensional subspaces, supplementing the methods of construction of Gaussian measures and infinite-product-type probability measures. This new method confirms that probability measures with this property are generic amongst probability measures that are not supported on finite-dimensional subspaces. In the process, we show the existence of an uncountable measurable family of independent vectors having the cardinality of the continuum in any infinite-dimensional Banach space. Comments: 7 pages Subjects: Functional Analysis (math.FA) ; Probability (math.PR) MSC classes: 46B09, 28A05, 03E10, 15A03, 11N05, 13A05 Cite as: arXiv:2512.21664 [math.FA] (or arXiv:2512.21664v4 [math.FA] for this version) https://doi.org/10.48550/arXiv.2512.21664 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nizar El Idrissi [ view email ] [v1] Thu, 25 Dec 2025 13:12:11 UTC (6 KB) [v2] Thu, 29 Jan 2026 09:53:50 UTC (7 KB) [v3] Mon, 16 Feb 2026 14:13:43 UTC (7 KB) [v4] Mon, 24 Aug 2026 22:49:55 UTC (7 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2025-12 Change to browse by: math math.PR References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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