Some new results on integration for multifunction

Luisa Di Piazza, Domenico Candeloro, Kazimierz Musiał, Anna Rita Sambucini

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10 Citations (Scopus)


It has been proven in Di Piazza and Musiał (Set Valued Anal 13:167–179, 2005, Vector measures, integration and related topics, Birkhauser Verlag, Basel, vol 201, pp 171–182, 2010) that each Henstock–Kurzweil–Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable (Theorem 3.4). Moreover, in case of strongly measurable (multi)functions, a characterization of the Birkhoff integrability is given using a kind of Birkhoff strong property.
Original languageEnglish
Pages (from-to)361-372
Number of pages12
JournalRicerche di Matematica
Publication statusPublished - 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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    Di Piazza, L., Candeloro, D., Musiał, K., & Sambucini, A. R. (2018). Some new results on integration for multifunction. Ricerche di Matematica, 67, 361-372.