Decompositions of Weakly Compact Valued Integrable Multifunctions

Luisa Di Piazza and Kazimierz Musiał
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Luisa Di Piazza: Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy
Kazimierz Musiał: Institut of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Mathematics, 2020, vol. 8, issue 6, 1-13

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.

Keywords: gauge multivalued integral; scalarly defined multivalued integral; decomposition of a multifunction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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