Decompositions of Weakly Compact Valued Integrable Multifunctions

Luisa Di Piazza, Kazimierz Musiał

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We give a short overview on the decomposition property for integrable multifunctions, i.e., when an "integrable in a certain sense" multifunction can be represented as a sum of one of its integrable selections and a multifunction integrable in a narrower sense. The decomposition theorems are important tools of the theory of multivalued integration since they allow us to see an integrable multifunction as a translation of a multifunction with better properties. Consequently, they provide better characterization of integrable multifunctions under consideration. There is a large literature on it starting from the seminal paper of the authors in 2006, where the property was proved for Henstock integrable multifunctions taking compact convex values in a separable Banach space X. In this paper, we summarize the earlier results, we prove further results and present tables which show the state of art in this topic
Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalMathematics
Volume8
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • General Mathematics

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