1Mathematical Institute Slovak Academy of Sciences Bratislava, Slovakia 2Departamento de Matemáticas Facultad de Ciencias Universidad de los Andes Mérida 5101, Venezuela
Studia Mathematica, Tome 164 (2004) no. 3, pp. 205-229
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.
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
Affiliations des auteurs :
I. Dobrakov
1
;
T. V. Panchapagesan
2
1
Mathematical Institute Slovak Academy of Sciences Bratislava, Slovakia
2
Departamento de Matemáticas Facultad de Ciencias Universidad de los Andes Mérida 5101, Venezuela
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author = {I. Dobrakov and T. V. Panchapagesan},
title = {A generalized {Pettis} measurability criterion
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and integration of vector functions
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I. Dobrakov; T. V. Panchapagesan. A generalized Pettis measurability criterion
and integration of vector functions. Studia Mathematica, Tome 164 (2004) no. 3, pp. 205-229. doi: 10.4064/sm164-3-1
