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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Spectral orders, uniform integrability and Lebesgue's dominated convergence theorem


Author: Kong Ming Chong
Journal: Trans. Amer. Math. Soc. 191 (1974), 395-404
MSC: Primary 28A25
MathSciNet review: 0369646
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Abstract: Using the 'spectral' order relations $ \prec $ and $ \prec\prec$ introduced by Hardy, Littlewood and Pólya, we characterize the uniform integrability of a family of integrable functions. We also prove an extension and a 'converse' of the classical Lebesgue's dominated convergence theorem in terms of the 'spectral' orders $ \prec $ and $ \prec\prec$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0369646-2
PII: S 0002-9947(1974)0369646-2
Keywords: Spectral orders, uniform integrability, equimeasurability, decreasing rearrangements, relatively weak compactness, nonatomic measure, closed convex hull, Lebesgue's dominated convergence theorem
Article copyright: © Copyright 1974 American Mathematical Society