Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Kazimierz Musiał

Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

musial@math.uni.wroc.pl

Keywords

  • Multifunctions
  • multimeasures
  • approximation
  • set-valued Pettis integral
  • support functions
  • selections
  • martingales

Mathematics Subject Classification

28B20; 28B05, 46G10, 54C60, 54C65

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Suggested citation

K. Musiał. “Approximation of Pettis Integrable Multifunctions with Values in Arbitrary Banach Spaces.” Journal of Convex Analysis 20 (2013), No. 3, 833–870. https://doi.org/10.68381/jca20045

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press LLC.