On the strong McShane integral of functions with values in a Banach space

Schwabik, Štefan, and Guoju, Ye. "On the strong McShane integral of functions with values in a Banach space." Czechoslovak Mathematical Journal 51.4 (2001): 819-828. <http://eudml.org/doc/30673>.

@article{Schwabik2001,
abstract = {The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.},
author = {Schwabik, Štefan, Guoju, Ye},
journal = {Czechoslovak Mathematical Journal},
keywords = {Bochner integral; strong McShane integral; Bochner integral; strong McShane integral},
language = {eng},
number = {4},
pages = {819-828},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the strong McShane integral of functions with values in a Banach space},
url = {http://eudml.org/doc/30673},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Schwabik, Štefan
AU - Guoju, Ye
TI - On the strong McShane integral of functions with values in a Banach space
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 4
SP - 819
EP - 828
AB - The classical Bochner integral is compared with the McShane concept of integration based on Riemann type integral sums. It turns out that the Bochner integrable functions form a proper subclass of the set of functions which are McShane integrable provided the Banach space to which the values of functions belong is infinite-dimensional. The Bochner integrable functions are characterized by using gauge techniques. The situation is different in the case of finite-dimensional valued vector functions.
LA - eng
KW - Bochner integral; strong McShane integral; Bochner integral; strong McShane integral
UR - http://eudml.org/doc/30673
ER -