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

Weak compactness and convergences in L¹_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, 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 (L¹_E'[E], Ñ₁) of weak*-scalarly integrable E'-valued functions via the Banach space (L^1,ρ_E'[E], N_1,ρ) associated to the lifting 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