We prove that several results of Talagrand proved for the Pettis integral hold true also for the Kurzweil--Henstock--Pettis integral. In particular the Kurzweil--Henstock--Pettis integrability can be characterized by suitable properties of the operators defined by the integrands and by cores of those functions.
DI PIAZZA L, MUSIAL K (2006). Characterizations of Kurzweil--Henstock--Pettis integrable functions. STUDIA MATHEMATICA, 176(2), 159-176 [10.4064/sm176-2-4].
Characterizations of Kurzweil--Henstock--Pettis integrable functions
DI PIAZZA, Luisa;
2006-01-01
Abstract
We prove that several results of Talagrand proved for the Pettis integral hold true also for the Kurzweil--Henstock--Pettis integral. In particular the Kurzweil--Henstock--Pettis integrability can be characterized by suitable properties of the operators defined by the integrands and by cores of those functions.
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