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An extension of the Vitali-Hahn-Saks Theorem

Author(s): Onésimo Hernández-Lerma; Jean B. Lasserre
Journal: Proc. Amer. Math. Soc. 124 (1996), 3673-3676.
MSC (1991): Primary 28A33; Secondary 28C15
Correction(s): Proc. Amer. Math. Soc. 126 (1998), no. 3, 949.
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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.

References:

1.
P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1968. MR 38:1718
2.
J.L. Doob, Measure Theory, Springer-Verlag, New York, 1994. MR 95c:28001
3.
O. Hernández-Lerma and J.B. Lasserre, Existence of solutions to the Poisson equation in $L^p$ spaces, LAAS Technical report 95045, Toulouse, 1995.
4.
H.L. Royden, Real Analysis, 3rd Edition, Macmillan, New York, 1988. MR 90g:00004
5.
W. Rudin, Real and Complex Analysis, 3rd edition, McGraw-Hill, New York, 1986. MR 87f:00009

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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: 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
Copyright of article: Copyright 1996, American Mathematical Society

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