An exact Fatou lemma for Gelfand integrals: a characterization of the Fatou property

An exact Fatou lemma for Gelfand integrals: a characterization of the Fatou property We establish an exact version of Fatou’s lemma for Gelfand integrals of functions and multifunctions in dual Banach spaces without any order structure, and under the saturation property on the underlying measure space. The necessity and sufficiency of saturation for the Fatou property is demonstrated. Our result has a direct application to the equilibrium existence result for saturated economies without convexity assumptions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

An exact Fatou lemma for Gelfand integrals: a characterization of the Fatou property

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Publisher
Springer International Publishing
Copyright
Copyright © 2015 by Springer Basel
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.
10.1007/s11117-015-0359-z
Publisher site
See Article on Publisher Site

Abstract

We establish an exact version of Fatou’s lemma for Gelfand integrals of functions and multifunctions in dual Banach spaces without any order structure, and under the saturation property on the underlying measure space. The necessity and sufficiency of saturation for the Fatou property is demonstrated. Our result has a direct application to the equilibrium existence result for saturated economies without convexity assumptions.

Journal

PositivitySpringer Journals

Published: Aug 21, 2015

References

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