Decomposability and uniform integrability in Pettis integration

Abstract

In this paper, we give several characterizations of decomposable subsets of the space of Pettis integrable functions (in particular, a characterization similar to that already known in the Bochner integrability setting). We also introduce the notion WPUI of uniform integrability, and obtain some relations between decomposability and PUI, resp. WPUI uniform integrability concepts. As consequence, conditional weak compactness and sequential weak compactness criteria are given under decomposability assumptions. Finally, an application to second order differential inclusions is presented.

Keywords: Pettis integral, decomposability, set-valued integral, uniform integrability, sequential weak compactness, differential inclusion

Quaestiones Mathematicae 29(2006), 39–58