Journal of Convex Analysis 20 (2013), No. 3, 833--870
Copyright Heldermann Verlag 2013
Approximation of Pettis Integrable Multifunctions with Values in Arbitrary Banach Spaces
Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4, 50-384 Wroclaw, Poland
Approximation of functions and multifunctions by simple functions and multifunctions plays an important role in the theory separable valued functions and multifunctions. Also in case of Pettis integrable functions with values in non-separable Banach spaces there exists a satisfactory approximation theory, but in case of Pettis integrable multifunctions with values in non-separable Banach spaces no such a theory exists. It is the aim of this paper to fill in that gap.
Keywords: Multifunctions, multimeasures, approximation, set-valued Pettis integral, support functions, selections, martingales.
MSC: 28B20; 28B05, 46G10, 54C60, 54C65
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