Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616525 | Journal of Mathematical Analysis and Applications | 2013 | 13 Pages |
Abstract
The aim of this paper is to describe Henstock-Kurzweil-Pettis (HKP) integrable compact valued multifunctions. Such characterizations are known in case of functions (see Di Piazza and MusiaÅÂ (2006)Â [16]). It is also known (see Di Piazza and MusiaÅÂ (2010)Â [19]) that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in the theory by weakly sequentially complete Banach spaces and by spaces possessing the Schur property.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Luisa Di Piazza, Kazimierz MusiaÅ,