The non-Archimedean analogs of the Bochner-Kolmogorov, Minlos-Sazonov   and Kakutani theorems
  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. 
S.V. Ludkovsky