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Title: A general Fatou Lemma
Authors: Loeb, P.A.
Sun, Y. 
Keywords: Fatou Lemma
Game theory
Gelfand integral
Nonstandard analysis
Pure strategy equilibrium
Vector Loeb space
Issue Date: 2007
Citation: Loeb, P.A., Sun, Y. (2007). A general Fatou Lemma. Advances in Mathematics 213 (2) : 741-762. ScholarBank@NUS Repository.
Abstract: A general Fatou Lemma is established for a sequence of Gelfand integrable functions from a vector Loeb space to the dual of a separable Banach space or, with a weaker assumption on the sequence, a Banach lattice. A corollary sharpens previous results in the finite-dimensional setting even for the case of scalar measures. Counterexamples are presented to show that the results obtained here are sharp in various aspects. Applications include systematic generalizations of the distribution of correspondences from the case of scalar Loeb spaces to the case of vector Loeb spaces and a proof of the existence of a pure strategy equilibrium in games with private and public information and with compact metric action spaces.©2007 Elsevier Inc. All rights reserved.
Source Title: Advances in Mathematics
ISSN: 00018708
DOI: 10.1016/j.aim.2007.01.008
Appears in Collections:Staff Publications

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