Quasi-invariant and pseudo-differentiable measures on a non-Archimedean Banach space.I. Real-valued measures

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 in $\bf R$.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 also are considered.Convergence of quasi-invariant and pseudo-differentiable measures in thecorresponding spaces of measures is investigated.