Geodesic
Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions
Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 211-223

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We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ 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.
We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ 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.
DOI : 10.21136/MB.2006.134086
Classification : 26A39, 26A42, 26A45, 28B05
Keywords: Kurzweil-Henstock integral; Kurzweil-Henstock-Pettis integral; Pettis integral 
Bongiorno, B.; Di Piazza, Luisa; Musiał, K. Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions. Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 211-223. doi: 10.21136/MB.2006.134086
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