A counterexample to “An extension of the Vitali-Hahn-Saks theorem” and a compactness result

Degla, Guy

doi:10.1090/S0002-9939-00-05411-3

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 $\mathbf {R}^n$.

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