Adv. Math. Econ. Volume 3, pp.1-44 (2001)

Weak compactness and convergences in L^{1}_{E'}[E]

Houcine Benabdellah and Charles Castaing

Département de Mathématiques, Université Cadi Ayyad, Faculté des Sciences Semlalia, B.P. S15, Marrakech, Maroc Département de Mathématiques, case 051, Université Montpellier II, F-34095 Montpellier cedex 5, France

- Suppose that
(Ω,F, μ)is a complete probability space,Eis a Banach space,E'is the topological dual ofEandρis a lifting in L. We state several convergences and weak compactness results in the Banach space^{∞}(μ)(Lof weak*-scalarly integrable^{1}_{E'}[E], Ñ_{1})E'-valued functions via the Banach space(Lassociated to the lifting^{1,ρ}_{E'}[E], N_{1,ρ})ρ. Applications to Young measures, Mathematical Economics, Minimization problems and Set-valued integration are also presented.

- compact, conditionally weakly compact, Fatou, lifting, tight, Young measure