Geodesic
Integration of Multifunctions with Closed Convex Values in Arbitrary Banach Spaces
Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1233-1246
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Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We prove that positive Denjoy-Pettis integrable multifunctions are Pettis integrable and we obtain a full description of McShane integrability in terms of Henstock and Pettis integrability, finishing the problem started by D. H. Fremlin in 1994 [The Henstock and McShane integrals of vector-valued functions, Illinois J. Math. 38(3) (1994) 471--479].
Classification : 28B20, 26E25, 26A39, 28B0, 46G10, 54C60, 54C65
Mots-clés : Positive multifunction, gauge integral, decomposition theorem for multifunction, selection, measure theory 
@article{JCA_2020_27_4_JCA_2020_27_4_a8,
     author = {D. Candeloro and L. Di Piazza and K. Musial and A. R. Sambucini},
     title = {Integration of {Multifunctions} with {Closed} {Convex} {Values} in {Arbitrary} {Banach} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {1233--1246},
     year = {2020},
     volume = {27},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a8/}
}
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D. Candeloro; L. Di Piazza; K. Musial; A. R. Sambucini. Integration of Multifunctions with Closed Convex Values in Arbitrary Banach Spaces. Journal of convex analysis, Tome 27 (2020) no. 4, pp. 1233-1246. http://geodesic.mathdoc.fr/item/JCA_2020_27_4_JCA_2020_27_4_a8/