Fatou's Lemma for Gelfand Integrable Mappings

Fatou's Lemma for Gelfand Integrable Mappings 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Fatou's Lemma for Gelfand Integrable Mappings

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2002 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1020292302718
Publisher site
See Article on Publisher Site

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.

Journal

PositivitySpringer Journals

Published: Oct 12, 2004

References

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