Integration of multifunctions with closed convex values in arbitrary\n Banach spaces

2018/12/03 by Domenico Candeloro, Candeloro, Domenico, Luisa Di Piazza +5
Computer Science · Mathematics · #26A39 #26E25 #28B0 #28B20 #46G10 #54C60 #54C65 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1812.00597

openalex publication_date 2018/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Integral properties of multifunctions with closed convex values are studied.\nIn this more general framework not all the tools and the technique used for\nweakly compact convex valued multifunctions work. We pay particular attention\nto the "positive multifunctions". Among them an investigation of multifunctions\ndetermined by vector-valued functions is presented. Finally, decomposition\nresults are obtained for scalarly and gauge-defined integrals of multifunctions\nand a full description of McShane integrability in terms of Henstock and Pettis\nintegrability is given.\n

Related

• On the integration of vector-valued functions
• Some Remarks on Vector-Valued Integration
• Selections of integrable multifunctions in arbitrary Banach spaces
• An axiomatic integral and a multivariate mean value theorem
• Toward an optimal theory of integration for quasi-Banach-space-valued\n functions