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Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space


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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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 149–199, 2003.

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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).

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  • Banach Space
  • Characteristic Functional
  • Infinite Product
  • Infinite Field
  • Kakutani Theorem