Henstock-type integrals are considered, for multifunctions taking values in the family of weakly compact and convex subsets of a Banach lattice . 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 -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.
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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. 363–383DOI 10.4171/RLM/710