Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

Luisa Di Piazza, Kazimierz Musiał

Risultato della ricerca: Articlepeer review

6 Citazioni (Scopus)

Abstract

The aim of this paper is to describe Henstock-Kurzweil-Pettis (HKP for short) integrable compact valued multifunctions. Such characterizations are known in case of functions. It is also known 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.
Lingua originaleEnglish
pagine (da-a)452-464
Numero di pagine13
RivistaJournal of Mathematical Analysis and Applications
Volume408
Stato di pubblicazionePublished - 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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