Variational Henstock integrability of Banach space valued functions
Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 287-296.

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We study the integrability of Banach space valued strongly measurable functions defined on $[0,1]$. In the case of functions $f$ given by $\sum \nolimits _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ are points of a Banach space and the sets $E_n$ 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 $\sum \nolimits _{n=1}^{\infty }x_n|E_n|$ 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.
DOI : 10.21136/MB.2016.19
Classification : 26A39
Keywords: Kurzweil-Henstock integral; variational Henstock integral; Pettis integral
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Di Piazza, Luisa; Marraffa, Valeria; Musiał, Kazimierz. Variational Henstock integrability of Banach space valued functions. Mathematica Bohemica, Tome 141 (2016) no. 2, pp. 287-296. doi : 10.21136/MB.2016.19. http://geodesic.mathdoc.fr/articles/10.21136/MB.2016.19/

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