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Positivity

, Volume 6, Issue 3, pp 297–315 | Cite as

Fatou's Lemma for Gelfand Integrable Mappings

  • B. Cornet
  • J.-P. Medecin
Article

Abstract

We provide a version of Fatou's lemma for mappings taking their values in E*, the topological dual of a separable Banach space. The mappings are assumed to be Gelfand integrable, a difference with previous papers, which, in infinite dimensional spaces, are mainly considering Bochner integrable mappings. This result is motivated by a general equilibrium model with locations studied by Cornet and Medecin (1999) and directly applies to it, since the space E* considered by Cornet and Medecin is the space of (Radon) vector measures defined on a compact metric space.

Fatou's lemma Banach space dual space measure space weak-star integral Gelfand integral 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • B. Cornet
    • 1
  • J.-P. Medecin
    • 1
  1. 1.CERMSEM, Maison des Sciences EconomiquesUniversité Paris IParis Cedex 13France

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