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

Weak compactness and convergences in L1E'[E]

Houcine Benabdellah1 and Charles Castaing2
1 Département de Mathématiques, Université Cadi Ayyad, Faculté des Sciences Semlalia, B.P. S15, Marrakech, Maroc
2 Département de Mathématiques, case 051, Université Montpellier II, F-34095 Montpellier cedex 5, France
Suppose that (Ω, F, μ) is a complete probability space, E is a Banach space, E' is the topological dual of E and ρ is a lifting in L(μ). We state several convergences and weak compactness results in the Banach space (L1E'[E], Ñ1) of weak*-scalarly integrable E'-valued functions via the Banach space (L1,ρE'[E], N1,ρ) associated to the lifting ρ. Applications to Young measures, Mathematical Economics, Minimization problems and Set-valued integration are also presented.
Key Words:
compact, conditionally weakly compact, Fatou, lifting, tight, Young measure