Probability measure annihilating all finite-dimensional subspaces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910023751303168 |
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| author | Idrissi, Nizar El Zoubeir, Hicham |
| author_facet | Idrissi, Nizar El Zoubeir, Hicham |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21664 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Probability measure annihilating all finite-dimensional subspaces Idrissi, Nizar El Zoubeir, Hicham Functional Analysis Probability 46B09, 28A05, 28A09, 03E10, 15A03, 11N05, 13A05 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. |
| title | Probability measure annihilating all finite-dimensional subspaces |
| topic | Functional Analysis Probability 46B09, 28A05, 28A09, 03E10, 15A03, 11N05, 13A05 |
| url | https://arxiv.org/abs/2512.21664 |