We study the integrability of Banach valued strongly measurable functions defined on [0, 1]. In case of functions f given by P∞ n=1 xnχEn , where xn belong to a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for the Bochner and for the Pettis integrability of f (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
BONGIORNO B, DI PIAZZA L, MUSIAL K (2006). Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions. MATHEMATICA BOHEMICA, 131(2), 211-223.
Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions
BONGIORNO, Benedetto;DI PIAZZA, Luisa;
2006-01-01
Abstract
We study the integrability of Banach valued strongly measurable functions defined on [0, 1]. In case of functions f given by P∞ n=1 xnχEn , where xn belong to a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for the Bochner and for the Pettis integrability of f (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
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