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Fundam. Prikl. Mat., 2003, Volume 9, Issue 1, Pages 149–199 (Mi fpm718)  

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

S. V. Lyudkovskii

General Physics Institute named after A. M. Prokhorov, Russian Academy of Sciences

Abstract: 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 $\mathbf Q_p$ 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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English version:
Journal of Mathematical Sciences (New York), 2005, 128:6, 3428–3460

Bibliographic databases:

UDC: 512.625.5+517.987

Citation: S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, Fundam. Prikl. Mat., 9:1 (2003), 149–199; J. Math. Sci., 128:6 (2005), 3428–3460

Citation in format AMSBIB
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\by S.~V.~Lyudkovskii
\paper Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a~non-Archimedean Banach space
\jour Fundam. Prikl. Mat.
\yr 2003
\vol 9
\issue 1
\pages 149--199
\mathnet{http://mi.mathnet.ru/fpm718}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2072624}
\zmath{https://zbmath.org/?q=an:1073.46036}
\elib{http://elibrary.ru/item.asp?id=9068256}
\transl
\jour J. Math. Sci.
\yr 2005
\vol 128
\issue 6
\pages 3428--3460
\crossref{https://doi.org/10.1007/s10958-005-0280-2}
\elib{http://elibrary.ru/item.asp?id=13473888}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84903371435}


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  • Фундаментальная и прикладная математика
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