JournalsrlmVol. 26, No. 4pp. 363–383

Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures

  • Antonio Boccuto

    Università degli Studi di Perugia, Italy
  • Domenico Candeloro

    Università degli Studi di Perugia, Italy
  • Anna Rita Sambucini

    Università degli Studi di Perugia, Italy
Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures cover
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Abstract

Henstock-type integrals are considered, for multifunctions taking values in the family of weakly compact and convex subsets of a Banach lattice XX. The main tool to handle the multivalued case is a Rådström-type embedding theorem established by C. C. A. Labuschagne, A. L. Pinchuck, C. J. van Alten in 2007. In this way the norm and order integrals reduce to that of a single-valued function taking values in an MM-space, and new proofs are deduced for some decomposition results recently stated in two recent papers by Di Piazza and Musiał based on the existence of integrable selections.

Cite this article

Antonio Boccuto, Domenico Candeloro, Anna Rita Sambucini, Henstock multivalued integrability in Banach lattices with respect to pointwise non atomic measures. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 363–383

DOI 10.4171/RLM/710