Published: 2023-07-26

Probability on submetric spaces

Adam Jakubowski Logo ORCID

Abstract

A submetric space is a topological space with continuous metrics, generating a metric topology weaker than the original one (e.g. a separable Hilbert space with the weak topology).
We demonstrate that on submetric spaces there exists a theory of convergence in probability, in law etc. equally effective as the Probability Theory on metric spaces. In the theory on submetric spaces the central role is played by a version of the Skorokhod almost sure representation, proved by the author some 25 years ago and in 2010 rediscovered by specialists in stochastic partial differential equations in the form of “stochastic compactness method”.

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Jakubowski, A. (2023). Probability on submetric spaces. Annales Mathematicae Silesianae, 37(2), 138–148. Retrieved from https://journals.us.edu.pl/index.php/AMSIL/article/view/15792

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Domyślna okładka

Vol. 37 No. 2 (2023)
Published: 2023-09-21


ISSN: 0860-2107
eISSN: 2391-4238
Ikona DOI 10.1515/amsil

Publisher
University of Silesia Press

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