A generalized Pettis measurability criterion and integration of vector functions

I. Dobrakov¹ ; T. V. Panchapagesan²

¹ Mathematical Institute Slovak Academy of Sciences Bratislava, Slovakia
² Departamento de Matemáticas Facultad de Ciencias Universidad de los Andes Mérida 5101, Venezuela

Studia Mathematica, Tome 164 (2004) no. 3, pp. 205-229

Résumé

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.

Détail

DOI : 10.4064/sm164-3-1

Keywords: banach space valued functions concepts mathcal measurability lambda measurability measurability defined where mathcal delta ring subsets nonvoid set lambda sigma subadditive submeasure sigma mathcal operator valued measure mathcal various characterizations given mathcal measurable resp lambda measurable measurable vector functions using other auxiliary results proved here basic theorems rigorously established