Geodesic
Gelfand Integral of Multifunctions
Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1193-12.

Voir la notice de l'article provenant de la source Heldermann Verlag

It has been proven by Cascales, Kadets and Rodriguez [J. Convex Anal. 18 (2011), 873-895] that each weak* scalarly integrable multifunction (with respect to a probability measure μ, whose values are compact convex subsets of a conjugate Banach space X* and the family of support functions determined by X is order bounded in L1(μ), is Gelfand integrable in the family of weakly compact convex subsets of X*. A question has been posed whether a similar result holds true for multifunctions with weakly compact convex values. We prove that the answer is affirmative if X does not contain any isomorphic copy of l1. If moreover the multifunction is compact valued, then it is Gelfand integrable in the family of compact convex subsets of X*.
Classification : 28B20, 28B05, 46G10, 54C60
Mots-clés : Multifunction, Gelfand set-valued integral, Pettis set-valued integral, support function 
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     author = {K. Musial},
     title = {Gelfand {Integral} of {Multifunctions}},
     journal = {Journal of convex analysis},
     pages = {1193--12},
     publisher = {mathdoc},
     volume = {21},
     number = {4},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a13/}
}
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K. Musial. Gelfand Integral of Multifunctions. Journal of convex analysis, Tome 21 (2014) no. 4, pp. 1193-12. http://geodesic.mathdoc.fr/item/JCA_2014_21_4_JCA_2014_21_4_a13/