Volume no :17, Issue no: 1, -2 September and October 2012

Journal of Mathematical Sciences: Advances and Applications

SPACES FOR RELATIVELY WEAKLY COMPACT VECTOR MEASURES AND S-COMPACT SET-VALUED MEASURES

Author's: GABRIEL BIRAME NDIAYE and DOUDOU SAKHIR THIAM
Pages: [65] - [87]
Received Date: August 19, 2010
Submitted by:

Abstract

We introduce a new concept of spaces, for a s-compact set-valued measure or set-valued Radon measure, a relatively weakly compact vector measure, or a weakly compact vector Radon measure. We establish that the quotient spaces are reflexive Banach spaces, since there norms are uniformly convex. We prove that these spaces are also uniformly smooths, therefore there norms are uniformly strongly differentiable.

Keywords

convex analysis, integration, set-valued measures, integral of Daniell.