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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

Yu. N. Vladimirskiĭ

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:

Received: 03.03.1977

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
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\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
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\transl
\jour Theory Probab. Appl.
\yr 1980
\vol 24
\issue 3
\pages 582--587
\crossref{https://doi.org/10.1137/1124067}
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