A counterexample to “An extension of the Vitali-Hahn-Saks theorem” and a compactness result
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- by Guy Degla PDF
- Proc. Amer. Math. Soc. 128 (2000), 2553-2559 Request permission
Abstract:
We give a counterexample to “An extension of the Vitali-Hahn-Saks theorem” and from that highlight the sharp frame within which any attempt to change the version of such an extension should be possible. Lastly a sequential compactness criterion for Radon measures absolutely continuous with respect to a prescribed Radon measure defined on a locally compact separable metric space (taking into account the ideas of Hernandez-Lerma and Lasserre) is proved. The results deal with Radon measures but yield obvious corollaries on real (or vector-valued) Radon measures and so on functions with bounded variation on open subsets of $\mathbf {R}^n$.References
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Additional Information
- Guy Degla
- Affiliation: Internatinal School for Advanced Studies (SISSA-ISAS), Via Beirut 2-4, 34014 Trieste, Italy
- Email: degla@sissa.it
- Received by editor(s): October 1, 1998
- Published electronically: February 29, 2000
- Communicated by: Christopher D. Sogge
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2553-2559
- MSC (2000): Primary 28A33; Secondary 28C15
- DOI: https://doi.org/10.1090/S0002-9939-00-05411-3
- MathSciNet review: 1676360