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Title: Integration of correspondences on loeb spaces
Authors: Sun, Y. 
Keywords: Bochner integral
Gel'fand integral
Loeb spaces
Weak compactness
Issue Date: 1997
Citation: Sun, Y. (1997). Integration of correspondences on loeb spaces. Transactions of the American Mathematical Society 349 (1) : 129-153. ScholarBank@NUS Repository.
Abstract: We study the Bochner and Gel'fand integration of Danach space valued correspondences on a general Loeb space. Though it is well known that the Lyapunov type result on the compactness and convexity of the integral of a correspondence and the Fatou type result on the preservation of upper semicontinuity by integration are in general not valid in the setting of an infinite dimensional space, we show that exact versions of these two results hold in the case we study. We also note that our results on a hyperfinite Loeb space capture the nature of the corresponding asymptotic results for the large finite case; but the unit Lebesgue interval fails to provide such a framework. © 1997 American Mathematical Society.
Source Title: Transactions of the American Mathematical Society
ISSN: 00029947
Appears in Collections:Staff Publications

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