FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2003, VOLUME 9, NUMBER 1, PAGES 149-199

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

S.
V.
Ludkovsky

Abstract

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Quasi-invariant and pseudo-differentiable measures on a Banach
space $X$ over
a non-Archimedean locally compact infinite field with
a non-trivial valuation are defined and constructed.
Measures are considered with values in non-Archimedean fields, for
example, the field $$**Q**_{p}
of $p$-adic numbers.
Theorems and criteria are formulated and proved about quasi-invariance
and pseudo-differentiability of measures relative to linear and
non-linear operators on $X$.
Characteristic functionals of measures are studied.
Moreover, the non-Archimedean analogs of the
Bochner--Kolmogorov and Minlos--Sazonov theorems are
investigated.
Infinite products of measures are considered and the analog of the
Kakutani theorem is proved.
Convergence of quasi-invariant and pseudo-differentiable measures in
the corresponding spaces of measures is investigated.

Location: http://mech.math.msu.su/~fpm/eng/k03/k031/k03111h.htm

Last modified: April 4, 2004.