
Journal of Convex Analysis 20 (2013), No. 3, 833870 Copyright Heldermann Verlag 2013 Approximation of Pettis Integrable Multifunctions with Values in Arbitrary Banach Spaces Kazimierz Musial Institute of Mathematics, University of Wroclaw, Pl. Grunwaldzki 2/4, 50384 Wroclaw, Poland musial@math.uni.wroc.pl 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 nonseparable Banach spaces there exists a satisfactory approximation theory, but in case of Pettis integrable multifunctions with values in nonseparable Banach spaces no such a theory exists. It is the aim of this paper to fill in that gap. Keywords: Multifunctions, multimeasures, approximation, setvalued Pettis integral, support functions, selections, martingales. MSC: 28B20; 28B05, 46G10, 54C60, 54C65 [ Fulltextpdf (289 KB)] for subscribers only. 