Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space. II. Measures with values in non-Archimedean fields

摘要

Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ overa non-Archimedean locally compact infinite field with a non-trivial valuationare defined and constructed. Measures are considered with values innon-Archimedean fields, for example, the field $\bf Q_p$ of $p$- adic numbers.Theorems and criteria are formulated and proved about quasi-invariance andpseudo-differentiability of measures relative to linear and non-linearoperators on $X$. Characteristic functionals of measures are studied. Moreover,the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonovtheorems are investigated. Infinite products of measures are considered and theanalog of the Kakutani theorem is proved. Convergence of quasi-invariant andpseudo-differentiable measures in the corresponding spaces of measures isinvestigated.