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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.

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

  • 1. Patrick Billingsley, Convergence of probability measures, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0233396
  • 2. J. L. Doob, Measure theory, Graduate Texts in Mathematics, vol. 143, Springer-Verlag, New York, 1994. MR 1253752
  • 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 ed., Macmillan Publishing Company, New York, 1988. MR 1013117
  • 5. Walter Rudin, Analiza rzeczywista i zespolona, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1986 (Polish). Translated from the English by Antoni Pierzchalski and Paweł Walczak. MR 850722

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Additional Information

Onésimo Hernández-Lerma
Affiliation: Departamento de Matemáticas, CINVESTAV-IPN, Apdo. Postal 14-740, México D.F. 07000, Mexico

Jean B. Lasserre
Affiliation: LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France

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