S-uniform scalar integrability and strong laws of large numbers for Pettis integrable functions with values in a separable locally convex space
Résumé
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 $E$.