The Gelfand Integral for Multi-Valued Functions

作者：Cascales B^*; Kadets V; Rodriguez J

来源：Journal of Convex Analysis, 2011, 18(3): 873-895.

• Multi-function
• measurable selector
• Gelfand integral for multi-functions
• Dunford integral for multi-functions
• Pettis integral for multi-functions

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.

• 出版日期2011