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.
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Ludkovsky, S.V. Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space. J Math Sci 128, 3428–3460 (2005). https://doi.org/10.1007/s10958-005-0280-2
- Banach Space
- Characteristic Functional
- Infinite Product
- Infinite Field
- Kakutani Theorem