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

Abstract

Measures on a non-Archimedean Banach space $X$ are considered with values in the real field $\mathbf{R}$ 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.

32 pages, AMS subject classification: 28C20 and 46S10