Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Lee, Tuo-Yeong. "Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion." Mathematica Bohemica 130.4 (2005): 349-354. <http://eudml.org/doc/249574>.

@article{Lee2005,
abstract = {It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f \: [0,1]^2 \longrightarrow \{\mathbb \{R\}\}$ and a continuous function $F \: [0,1]^2 \longrightarrow \{\mathbb \{R\}\}$ such that \[ (¶) \int \_0^x \bigg \lbrace (¶) \int \_0^yf(u,v) \mathrm \{d\}v \bigg \rbrace \mathrm \{d\}u = (¶) \int \_0^y \bigg \lbrace (¶) \int \_0^xf(u,v) \mathrm \{d\}u \bigg \rbrace \mathrm \{d\}v = F(x,y) \] for all $(x,y) \in [0,1]^2$.},
author = {Lee, Tuo-Yeong},
journal = {Mathematica Bohemica},
keywords = {Henstock-Kurzweil integral; McShane integral; Henstock-Kurzweil integral; McShane integral},
language = {eng},
number = {4},
pages = {349-354},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion},
url = {http://eudml.org/doc/249574},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Lee, Tuo-Yeong
TI - Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 4
SP - 349
EP - 354
AB - It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$-dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f \: [0,1]^2 \longrightarrow {\mathbb {R}}$ and a continuous function $F \: [0,1]^2 \longrightarrow {\mathbb {R}}$ such that \[ (¶) \int _0^x \bigg \lbrace (¶) \int _0^yf(u,v) \mathrm {d}v \bigg \rbrace \mathrm {d}u = (¶) \int _0^y \bigg \lbrace (¶) \int _0^xf(u,v) \mathrm {d}u \bigg \rbrace \mathrm {d}v = F(x,y) \] for all $(x,y) \in [0,1]^2$.
LA - eng
KW - Henstock-Kurzweil integral; McShane integral; Henstock-Kurzweil integral; McShane integral
UR - http://eudml.org/doc/249574
ER -