The non-Archimedean analogs of the Bochner-Kolmogorov, Minlos-Sazonov and Kakutani theorems

TL;DR

This paper develops non-Archimedean analogs of classical measure theorems, extending foundational results like Bochner-Kolmogorov, Minlos-Sazonov, and Kakutani to non-Archimedean Banach spaces and measures.

Contribution

It introduces non-Archimedean versions of key measure theorems and studies infinite product measures, expanding the theoretical framework of non-Archimedean analysis.

Findings

Established non-Archimedean Bochner-Kolmogorov theorem

Derived non-Archimedean Minlos-Sazonov theorem

Investigated non-Archimedean Kakutani theorem for product measures

Abstract

Measures on a non-Archimedean Banach space $X$ are considered with values in the real field $\bf R$ and in the non- Archimedean fields. The non-Archimedean analogs of the Bochner- Kolmogorov and Minlos-Sazonov theorems are given. Moreover, infinite products of measures are studied and the analog of the Kakutani theorem is investigated.