In this paper we extend the Kolmogorov strong law of large numbers to random variables taking their values in a 2-uniformly smooth Banach space $(B, \| \|)$. In our result, the convergence of the classical series of variances is replaced by the convergence of the series having general term $\sup\{Ef^2(X_n)/n^2: \|f\|_{B'} \leq 1\}.$
Publié le : 1984-08-14
Classification:
Strong law of large numbers,
type 2 space,
2-uniformly smooth Banach space,
60B12,
46B20
@article{1176993233,
author = {Heinkel, Bernard},
title = {On the Law of Large Numbers in 2-Uniformly Smooth Banach Spaces},
journal = {Ann. Probab.},
volume = {12},
number = {4},
year = {1984},
pages = { 851-857},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993233}
}
Heinkel, Bernard. On the Law of Large Numbers in 2-Uniformly Smooth Banach Spaces. Ann. Probab., Tome 12 (1984) no. 4, pp. 851-857. http://gdmltest.u-ga.fr/item/1176993233/