Using partitions of the unity ($(PU)$-partition), a new definition of an integral is given for a function f : [a, b] \to X, where X is a Banach space, and it is proved that this integral is equivalent to the Bochner integral.
@article{37,
title = {An integral for a Banach valued function},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v44i0.37},
language = {EN},
url = {http://dml.mathdoc.fr/item/37}
}
Riccobono, Giuseppa. An integral for a Banach valued function. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v44i0.37. http://gdmltest.u-ga.fr/item/37/