It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.
DI PIAZZA L, MUSIAL K (2005). Set valued Kurzweil-Henstock-Pettis integral. SET-VALUED ANALYSIS, 13(2), 167-179 [10.1007/s11228-004-0934-0].
Set valued Kurzweil-Henstock-Pettis integral
DI PIAZZA, Luisa;
2005-01-01
Abstract
It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.
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