Generalizing techniques developed by Cuesta and Matran for Bochner integrable random vectors of a separable Banach space, we prove a strong law of large numbers for Pettis integrable random elements of a separable locally convex space $E$. This result may be seen as a compactness result in a suitable topology on the set of Pettis integrable probabilities on $E$.
Publié le : 2000-07-05
Classification:
Strong law of large numbers,
Glivenko--Cantelli,
pairwise independent,
Pettis,
Skorokhod representation,
Pettis uniformly integrable,
Kantorovich functional,
Wasserstein metric,
Young measure,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR],
[MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]
@article{hal-00726636,
author = {Castaing, Charles and Raynaud de Fitte, Paul},
title = {S-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00726636}
}
Castaing, Charles; Raynaud de Fitte, Paul. S-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00726636/