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
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Quasi-invariant and pseudo-differentiable measures on a Banach
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
of -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 .
Characteristic functionals of measures are studied.
Moreover, the non-Archimedean analogs of the
Bochner--Kolmogorov and Minlos--Sazonov theorems are
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.
Last modified: April 4, 2004.