Analogues of the Marcinkiewicz-Zygmund and Rosenthal inequalities for Banach space valued random vectors are proved. As an application some results on the strong law of large numbers are obtained. It is proved that the Marcinkiewicz SLLN holds for every $p$-integrable, mean zero $B$-valued $\mathrm{rv}$ if and only if $B$ is of Rademacher type $p(1 \leq p < 2)$.
Publié le : 1981-02-14
Classification:
Marcinkiewicz-Zygmund inequality,
strong law of large numbers,
spaces of Rademacher type $p$,
60B05
@article{1176994517,
author = {Acosta, Alejandro De},
title = {Inequalities for $B$-Valued Random Vectors with Applications to the Strong Law of Large Numbers},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 157-161},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994517}
}
Acosta, Alejandro De. Inequalities for $B$-Valued Random Vectors with Applications to the Strong Law of Large Numbers. Ann. Probab., Tome 9 (1981) no. 6, pp. 157-161. http://gdmltest.u-ga.fr/item/1176994517/