Probability measure annihilating all finite-dimensional subspaces
Functional Analysis
2026-02-17 v3 Probability
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.
Cite
@article{arxiv.2512.21664,
title = {Probability measure annihilating all finite-dimensional subspaces},
author = {Nizar El Idrissi and Hicham Zoubeir},
journal= {arXiv preprint arXiv:2512.21664},
year = {2026}
}
Comments
7 pages