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A generalized Pettis measurability criterion and integration of vector functions

Tom 164 / 2004

Studia Mathematica 164 (2004), 205-229 MSC: Primary 28B05; Secondary 46E40, 46G10. DOI: 10.4064/sm164-3-1

Streszczenie

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.

Autorzy

• I. DobrakovMathematical Institute
Bratislava, Slovakia
• T. V. PanchapagesanDepartamento de Matemáticas
Mérida 5101, Venezuela
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