G-uniform scalar integrability and strong laws of large numbers for Pettisintegrable functions with values in a separable locally convex space

Generalizing techniques developed by Cuesta and Matran for Buchner integrab le random vectors of a separable Banach space, we prove a strong law of lar ge numbers for Pettis integrable random elements of a separable locally con vex space E. This result may be seen as a compactness result in a suitable topology on the set of Pettis integrable probabilities on E.