McShane equi-integrability and Vitali’s convergence theorem

Kurzweil, Jaroslav, and Schwabik, Štefan. "McShane equi-integrability and Vitali’s convergence theorem." Mathematica Bohemica 129.2 (2004): 141-157. <http://eudml.org/doc/249386>.

@article{Kurzweil2004,
abstract = {The McShane integral of functions $f\:I\rightarrow \mathbb \{R\}$ defined on an $m$-dimensional interval $I$ is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.},
author = {Kurzweil, Jaroslav, Schwabik, Štefan},
journal = {Mathematica Bohemica},
keywords = {McShane integral; Vitali convergence theorem; equi-integrability; McShane integral; Vitali convergence theorem; equi-integrability},
language = {eng},
number = {2},
pages = {141-157},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {McShane equi-integrability and Vitali’s convergence theorem},
url = {http://eudml.org/doc/249386},
volume = {129},
year = {2004},
}

TY - JOUR
AU - Kurzweil, Jaroslav
AU - Schwabik, Štefan
TI - McShane equi-integrability and Vitali’s convergence theorem
JO - Mathematica Bohemica
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 129
IS - 2
SP - 141
EP - 157
AB - The McShane integral of functions $f\:I\rightarrow \mathbb {R}$ defined on an $m$-dimensional interval $I$ is considered in the paper. This integral is known to be equivalent to the Lebesgue integral for which the Vitali convergence theorem holds. For McShane integrable sequences of functions a convergence theorem based on the concept of equi-integrability is proved and it is shown that this theorem is equivalent to the Vitali convergence theorem.
LA - eng
KW - McShane integral; Vitali convergence theorem; equi-integrability; McShane integral; Vitali convergence theorem; equi-integrability
UR - http://eudml.org/doc/249386
ER -