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1. Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions

Creator:
Bongiorno, B., Di Piazza, Luisa, and Musiał, Kazimierz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil-Henstock integral, Kurzweil-Henstock-Pettis integral, and Pettis integral
Language:
English
Description:
We study the integrability of Banach valued strongly measurable functions defined on [0, 1]. In case of functions f given by ∞∑ 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.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Variational Henstock integrability of Banach space valued functions

Creator:
Di Piazza, Luisa, Marraffa, Valeria, and Musiał, Kazimierz
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Kurzweil-Henstock integral, variational Henstock integral, and Pettis integral
Language:
English
Description:
We study the integrability of Banach space valued strongly measurable functions defined on [0, 1]. In the case of functions f given by ∑ ∞ n=1 xnχEn , where xn are points of a Banach space and the sets En are Lebesgue measurable and pairwise disjoint subsets of [0, 1], there are well known characterizations for Bochner and Pettis integrability of f. The function f is Bochner integrable if and only if the series ∑∞ n=1 xn|En| is absolutely convergent. Unconditional convergence of the series is equivalent to Pettis integrability of f. In this paper we give some conditions for variational Henstock integrability of a certain class of such functions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public