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arXiv · 2512.21664

Probability measure annihilating all finite-dimensional subspaces

Nizar El Idrissi·Hicham Zoubeir
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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.

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Nizar El Idrissi, Hicham Zoubeir. 2026-08-24. Probability measure annihilating all finite-dimensional subspaces. https://arxiv.org/abs/2512.21664

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