Variational Henstock integrability of Banach space valued functions

Di Piazza, Luisa, Marraffa, Valeria, and Musiał, Kazimierz. "Variational Henstock integrability of Banach space valued functions." Mathematica Bohemica 141.2 (2016): 287-296. <http://eudml.org/doc/276995>.

@article{DiPiazza2016,
abstract = {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.},
author = {Di Piazza, Luisa, Marraffa, Valeria, Musiał, Kazimierz},
journal = {Mathematica Bohemica},
keywords = {Kurzweil-Henstock integral; variational Henstock integral; Pettis integral},
language = {eng},
number = {2},
pages = {287-296},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Variational Henstock integrability of Banach space valued functions},
url = {http://eudml.org/doc/276995},
volume = {141},
year = {2016},
}

TY - JOUR
AU - Di Piazza, Luisa
AU - Marraffa, Valeria
AU - Musiał, Kazimierz
TI - Variational Henstock integrability of Banach space valued functions
JO - Mathematica Bohemica
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 141
IS - 2
SP - 287
EP - 296
AB - 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.
LA - eng
KW - Kurzweil-Henstock integral; variational Henstock integral; Pettis integral
UR - http://eudml.org/doc/276995
ER -