Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Fatou's identity
and Lebesgue's convergence theorem


Author: Heinz-Albrecht Klei
Journal: Proc. Amer. Math. Soc. 127 (1999), 2297-2302
MSC (1991): Primary 26D15, 28A20, 28A25
Published electronically: April 9, 1999
MathSciNet review: 1636974
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 26D15, 28A20, 28A25

Retrieve articles in all journals with MSC (1991): 26D15, 28A20, 28A25


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: http://dx.doi.org/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
Published electronically: April 9, 1999
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society