Abstract

Integral properties of multifunctions with closed convex values are studied. In this more general framework not all the tools and the technique used for weakly compact convex valued multifunctions work. We prove that positive Denjoy-Pettis integrable multifunctions are Pettis integrable and we obtain a full description of McShane integrability in terms of Henstock and Pettis integrability, finishing the problem started by D. H. Fremlin in 1994 [The Henstock and McShane integrals of vector-valued functions, Illinois J. Math. 38(3) (1994) 471–479].

Author information

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

Luisa Di Piazza

Dept. of Mathematics and Computer Sciences, University of Palermo, 90123 Palermo, Italy

luisa.dipiazza@unipa.it

Anna Rita Sambucini

Dept. of Mathematics and Computer Sciences, University of Perugia, 06123 Perugia, Italy

anna.sambucini@unipg.it

Keywords

  • Positive multifunction
  • gauge integral
  • decomposition theorem for multifunction
  • selection
  • measure theory

Mathematics Subject Classification

28B20, 26E25, 26A39, 28B0, 46G10, 54C60, 54C65

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Suggested citation

D. Candeloro, L. Di Piazza, K. Musiał, A. R. Sambucini. “Integration of Multifunctions with Closed Convex Values in Arbitrary Banach Spaces.” Journal of Convex Analysis 27 (2020), No. 4, 1233–1246. https://doi.org/10.68381/jca27065

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Published by Heldermann Verlag, 2020. Rights now held by Banach Press LLC.