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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An extension
of the Vitali-Hahn-Saks Theorem


Authors: Onésimo Hernández-Lerma and Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 124 (1996), 3673-3676
MSC (1991): Primary 28A33; Secondary 28C15
MathSciNet review: 1401743
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Abstract: The Vitali-Hahn-Saks theorem on the absolute continuity of the setwise limit of a sequence of bounded measures is extended to allow unbounded measures and convergence of integrals of continuous functions vanishing at infinity.


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Additional Information

Onésimo Hernández-Lerma
Affiliation: Departamento de Matemáticas, CINVESTAV-IPN, Apdo. Postal 14-740, México D.F. 07000, Mexico
Email: ohernand@math.cinvestav.mx.

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France
Email: lasserre@laas.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03922-6
PII: S 0002-9939(96)03922-6
Keywords: Measures, setwise convergence, absolute continuity
Received by editor(s): January 24, 1995
Additional Notes: The research of the first author was partially supported by a visiting professorship at Paul Sabatier University, Toulouse, France, and by CONACYT Grant 1332-E9206
This research was partially supported by the CNRS (France)- CONACYT (México) Scientific Cooperation Program.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1996 American Mathematical Society