Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 351-357
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D. Kh. Mushtari. On almost sure convergence in linear spaces of random variables. Teoriâ veroâtnostej i ee primeneniâ, Tome 15 (1970) no. 2, pp. 351-357. http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a16/
@article{TVP_1970_15_2_a16,
author = {D. Kh. Mushtari},
title = {On almost sure convergence in linear spaces of random variables},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {351--357},
year = {1970},
volume = {15},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a16/}
}
TY - JOUR
AU - D. Kh. Mushtari
TI - On almost sure convergence in linear spaces of random variables
JO - Teoriâ veroâtnostej i ee primeneniâ
PY - 1970
SP - 351
EP - 357
VL - 15
IS - 2
UR - http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a16/
LA - ru
ID - TVP_1970_15_2_a16
ER -
%0 Journal Article
%A D. Kh. Mushtari
%T On almost sure convergence in linear spaces of random variables
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1970
%P 351-357
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/TVP_1970_15_2_a16/
%G ru
%F TVP_1970_15_2_a16
In this paper, almost sure convergence in a linear space $L$ of random variables with values in a normed space $\mathfrak X$ is considered. In case when $\mathfrak X=R$, it is shown that the necessary and sufficient condition for convergence in measure and a.s. convergence to coincide is nuclearity of $L$.
