A generalized Pettis measurability criterion and integration of vector functions
Volume 164 / 2004
Studia Mathematica 164 (2004), 205-229
MSC: Primary 28B05; Secondary 46E40, 46G10.
DOI: 10.4064/sm164-3-1
Abstract
For Banach-space-valued functions, the concepts of ${\mathcal P}$-measurability, $\lambda $-measurability and ${\bf m}$-measurability are defined, where ${\mathcal P}$ is a $\delta $-ring of subsets of a nonvoid set $T$, $\lambda $ is a $\sigma $-subadditive submeasure on $\sigma ({\mathcal P})$ and ${\bf m}$ is an operator-valued measure on ${\mathcal P}$. Various characterizations are given for ${\mathcal P}$-measurable (resp. $\lambda $-measurable, ${\bf m}$-measurable) vector functions on $T$. Using them and other auxiliary results proved here, the basic theorems of [6] are rigorously established.
