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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.
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.
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
 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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