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The McShane integral in weakly compactly generated spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Dec 2010Embargo end date: 01 Jan 2010 English Publisher:Elsevier BVJournal:Journal of Functional Analysis, volume 259, pages 2,776-2,792 (issn: 0022-1236, Copyright policy )
Authors: Avilés, A.; Plebanek, G.; Rodríguez, J.;

doi: 10.1016/j.jfa.2010.08.007 , 10.48550/arxiv.1001.4896

arXiv: 1001.4896

The McShane integral in weakly compactly generated spaces

Abstract

Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative.

Revised version. To appear in Journal of Functional Analysis

Related Organizations
Keywords

McShane integral, 28B05, 46B10, 46B26, Nonseparable Banach spaces, Probability (math.PR), scalarly null function, Filling family, Functional Analysis (math.FA), Mathematics - Functional Analysis, Scalarly null function, filling family, Pettis integral, FOS: Mathematics, Vector-valued set functions, measures and integrals, Vector-valued measures and integration, Analysis, Mathematics - Probability

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
8
Average
Average
Average
Green
hybrid