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Journal of Convex Analysis 19 (2012), No. 3, 671--683
Copyright Heldermann Verlag 2012

On Some Properties of Pettis Integrable Multifunctions

Nanda Dulal Chakraborty
Dept. of Mathematics, University of Burdwan, Burdwan 713104, West Bengal -- India

Tanusree Choudhury
Dept. of Mathematics, Raja Peary Mohan College, Calcutta University, Hooghly 712258, West Bengal -- India

We study Aumann-Pettis integrable multifunctions on 2X, where X is a separable Banach space and their integrals. We prove the existence of a weakly compact convex-valued Pettis integrable multifunction F for a closed, convex, decomposable and weakly sequentially compact subset K of P1(μ, X), the space of all Pettis integrable functions on X such that K coincides with SFP, the collection of all Pettis integrable selectors of F. We also study the weak compactness property of SFP.

Keywords: Aumann-Pettis integrable multifunctions, Pettis integrable multifunctions, Aumann-Pettis integral, Pettis integral, weak convergence.

MSC: 46G10, 46E30, 46P10; 28B20, 54C60

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