Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 574-579
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Yu. N. Vladimirskiǐ. On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure. Teoriâ veroâtnostej i ee primeneniâ, Tome 24 (1979) no. 3, pp. 574-579. http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a10/
@article{TVP_1979_24_3_a10,
author = {Yu. N. Vladimirskiǐ},
title = {On the conditions when the cylindrical measure on cojugate {Banach} space may be extended to {Radon} measure},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {574--579},
year = {1979},
volume = {24},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a10/}
}
TY - JOUR
AU - Yu. N. Vladimirskiǐ
TI - On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1979
SP - 574
EP - 579
VL - 24
IS - 3
UR - http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a10/
LA - ru
ID - TVP_1979_24_3_a10
ER -
%0 Journal Article
%A Yu. N. Vladimirskiǐ
%T On the conditions when the cylindrical measure on cojugate Banach space may be extended to Radon measure
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1979
%P 574-579
%V 24
%N 3
%U http://geodesic.mathdoc.fr/item/TVP_1979_24_3_a10/
%G ru
%F TVP_1979_24_3_a10
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.
