Relations among Henstock, McShane and Pettis integrals for multifunctions with compact convex values

Luisa Di Piazza, Kazimierz Musiał

Risultato della ricerca: Articlepeer review

12 Citazioni (Scopus)

Abstract

Fremlin [Ill J Math 38:471-479, 1994] proved that a Banach space valued function is McShane integrable if and only if it is Henstock and Pettis integrable. In this paper we prove that the result remains valid also in case of multifunctions with compact convex values being subsets of an arbitrary Banach space (see Theorem 3.4). Di Piazza and Musial [Monatsh Math 148:119-126, 2006] proved that if X is a separable Banach space, then each Henstock integrable multifunction which takes as its values convex compact subsets of X is a sum of a McShane integrable multifunction and a Henstock integrable function. Here we show that such a decomposition is true also in case of an arbitrary Banach space (see Theorem 3.3). We prove also that Henstock and McShane integrable multifunctions possess Henstock and McShane (respectively) integrable selections (see Theorem 3.1).
Lingua originaleEnglish
pagine (da-a)459-470
Numero di pagine12
RivistaMONATSHEFTE FÜR MATHEMATIK
Volume173
Stato di pubblicazionePublished - 2014

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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