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

Bongiorno, B., Di Piazza, Luisa, and Musiał, Kazimierz. "Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions." Mathematica Bohemica 131.2 (2006): 211-223. <http://eudml.org/doc/249908>.

@article{Bongiorno2006,
abstract = {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.},
author = {Bongiorno, B., Di Piazza, Luisa, Musiał, Kazimierz},
journal = {Mathematica Bohemica},
keywords = {Kurzweil-Henstock integral; Kurzweil-Henstock-Pettis integral; Pettis integral; Pettis integral},
language = {eng},
number = {2},
pages = {211-223},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions},
url = {http://eudml.org/doc/249908},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Bongiorno, B.
AU - Di Piazza, Luisa
AU - Musiał, Kazimierz
TI - Kurzweil-Henstock and Kurzweil-Henstock-Pettis integrability of strongly measurable functions
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 2
SP - 211
EP - 223
AB - 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.
LA - eng
KW - Kurzweil-Henstock integral; Kurzweil-Henstock-Pettis integral; Pettis integral; Pettis integral
UR - http://eudml.org/doc/249908
ER -