Geodesic
The Gelfand Integral for Multi-Valued Functions
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 873-895

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We study the existence of w*-scalarly measurable selectors and almost selectors for w*-scalarly measurable multi-functions with values in dual Banach spaces. These selection results are used to study Gelfand and Dunford integrals for multi-functions: our non separable setting extends previous studies that have been done for separable Banach spaces. Pettis integral for multi-functions, already studied by different authors, naturally appears as a particular case of Dunford integral. We also study when the Gelfand integral of a multi-function is not only w*-compact but w-compact.
Classification : 28B05, 28B20, 46G10
Mots-clés : Multi-function, measurable selector, Gelfand integral for multi-functions, Dunford integral for multi-functions, Pettis integral for multi-functions 
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B. Cascales; V. Kadets; J. Rodríguez. The Gelfand Integral for Multi-Valued Functions. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 873-895. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a17/