Weak compactness and convergences in LE’1[E]

  • Houcine Benabdellah
  • Charles Castaing
Part of the Advances in Mathematical Economics book series (MATHECON, volume 3)


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 (μ). We state several convergences and weak compactness results in the Banach space (L E’ 1 , [E], 1) of weak*-scalarly integrable E’-valued functions via the Banach space (L E’ 1,ρ , [E], 1,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 

Mathematics Subject Classification (2000)

46E40 28B05 28B20 


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Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Houcine Benabdellah
    • 1
  • Charles Castaing
    • 2
  1. 1.Département de Mathématiques, Faculté des Sciences SemlaliaUniversité Cadi AyyadMarrakechMaroc
  2. 2.Département de Mathématiques, case 051Université Montpellier IIMontpellier cedex 5France

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