Geodesic
A Remark on Characteristic Functionals
Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 2, pp. 201-205

Voir la notice de l'article provenant de la source Math-Net.Ru

For the case of separable Hilbert space $H$ two theorems are proved that give necessary and sufficient conditions for the functional $\chi(f)$, $f\in H$, to be the characteristic functional of some probability distribution of $H$. In the first theorem the case $\int{\|x\|}^2\,dP+\infty$ is investigated; the second one deals with the general case and the condition for it is given in the form of the continuity of $\chi(t)$ in the $\mathfrak J$-topology whose definition is contained in the paper. 
@article{TVP_1958_3_2_a7,
     author = {V. Sazonov},
     title = {A {Remark} on {Characteristic} {Functionals}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {201--205},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {1958},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1958_3_2_a7/}
}
TY  - JOUR
AU  - V. Sazonov
TI  - A Remark on Characteristic Functionals
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1958
SP  - 201
EP  - 205
VL  - 3
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1958_3_2_a7/
LA  - ru
ID  - TVP_1958_3_2_a7
ER  - 
%0 Journal Article
%A V. Sazonov
%T A Remark on Characteristic Functionals
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1958
%P 201-205
%V 3
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1958_3_2_a7/
%G ru
%F TVP_1958_3_2_a7
V. Sazonov. A Remark on Characteristic Functionals. Teoriâ veroâtnostej i ee primeneniâ, Tome 3 (1958) no. 2, pp. 201-205. http://geodesic.mathdoc.fr/item/TVP_1958_3_2_a7/