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Henstock–Kurzweil–Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space
Luisa Di PiazzaKazimierz Musiałsubject
Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)Henstock integralIntegrable systemApplied MathematicsBanach spaceconvergence theoremsFunction (mathematics)Characterization (mathematics)set-valued Henstock-Kurzweil-Pettis integralset-valued Pettis integralsupport functionMultifunctionSettore MAT/05 - Analisi MatematicaConvergence (routing)AnalysisselectorMathematicsdescription
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 Musial (2006) [16] ). It is also known (see Di Piazza and Musial (2010) [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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-12-01 | Journal of Mathematical Analysis and Applications |