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 Teor. Veroyatnost. i Primenen., 1979, Volume 24, Issue 3, Pages 574–579 (Mi tvp2642)

Short Communications

On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure

Kostroma

Abstract: In an arbitrary Banach space $E$ we define the local convex topologies $t_N(E)\ge t_S(E)$. Let $\lambda$ be an arbitrary cylindrical probability on $E'$. We prove that continuity of $\lambda$ with respect to $t_N(E)$ ($t_S(E)$) is a necessary (sufficient) condition for $\lambda$ may be extended to a Radon measure on $E'$. If $E$ is Hilbertian then the topologies $t_N(E)$ and $t_S(E)$ are identical to $J$-topology introduced by V. V. Sazonov. Conversely, if $t_N(E)=t_S(E)$ then $E$ is Hilbertian.

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English version:
Theory of Probability and its Applications, 1980, 24:3, 582–587

Bibliographic databases:

Citation: Yu. N. Vladimirskiǐ, “On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure”, Teor. Veroyatnost. i Primenen., 24:3 (1979), 574–579; Theory Probab. Appl., 24:3 (1980), 582–587

Citation in format AMSBIB
\Bibitem{Vla79}
\paper On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure
\jour Teor. Veroyatnost. i Primenen.
\yr 1979
\vol 24
\issue 3
\pages 574--579
\mathnet{http://mi.mathnet.ru/tvp2642}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=541369}
\zmath{https://zbmath.org/?q=an:0435.60009|0408.60005}
\transl
\jour Theory Probab. Appl.
\yr 1980
\vol 24
\issue 3
\pages 582--587
\crossref{https://doi.org/10.1137/1124067}