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

Di Piazza, L., & Musial, K. (2020). Decompositions of Weakly Compact Valued Integrable Multifunctions. MATHEMATICS, 8(6), 1-13 [10.3390/math8060863].

Decompositions of Weakly Compact Valued Integrable Multifunctions

Di Piazza, L
Membro del Collaboration Group
;
2020

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
Settore MAT/05 - Analisi Matematica
Di Piazza, L., & Musial, K. (2020). Decompositions of Weakly Compact Valued Integrable Multifunctions. MATHEMATICS, 8(6), 1-13 [10.3390/math8060863].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/427007
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