Fatou's Lemma for Gelfand Integrable Mappings

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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.

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