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ISSN 1088-6826(e) ISSN 0002-9939(p)

Fatou's identity and Lebesgue's convergence theorem

Author(s): Heinz-Albrecht Klei
Journal: Proc. Amer. Math. Soc. 127 (1999), 2297-2302.
MSC (1991): Primary 26D15, 28A20, 28A25
Posted: April 9, 1999
MathSciNet review: 1636974
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Abstract: The classical Fatou lemma for bounded sequences of nonnegative integrable functions is represented as an equality. A similar result is stated for measure convergent sequences. Neither result requires a uniform integrability assumption. For the latter a converse is proven. Two extensions of Lebesgue's convergence theorem are presented.

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Additional Information:

Heinz-Albrecht Klei
Affiliation: Département de Mathématiques et Informatique, Université de Reims, Moulin de la Housse, B.P. 1039, 51687 Reims Cedex 2, France
Email: heinz.klei@univ-reims.fr

DOI: 10.1090/S0002-9939-99-05099-6
PII: S 0002-9939(99)05099-6
Keywords: Fatou's lemma, Fatou's identity, Lebesgue's theorem, uniform integrability, measure convergent sequence, norm convergent sequence.
Received by editor(s): October 27, 1997
Posted: April 9, 1999
Communicated by: Frederick W. Gehring
Copyright of article: Copyright 1999, American Mathematical Society

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