For Banach-space-valued functions, the concepts of 𝒫-measurability, λ-measurability and m-measurability are defined, where 𝒫 is a δ-ring of subsets of a nonvoid set T, λ is a σ-subadditive submeasure on σ(𝒫) and m is an operator-valued measure on 𝒫. Various characterizations are given for 𝒫-measurable (resp. λ-measurable, m-measurable) vector functions on T. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-1,
author = {I. Dobrakov and T. V. Panchapagesan},
title = {A generalized Pettis measurability criterion and integration of vector functions},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {205-229},
zbl = {1058.28008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-1}
}
I. Dobrakov; T. V. Panchapagesan. A generalized Pettis measurability criterion and integration of vector functions. Studia Mathematica, Tome 162 (2004) pp. 205-229. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm164-3-1/