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RESEARCH PRODUCT
Kurzweil--Henstock and Kurzweil--Henstock--Pettis integrability of strongly measurable functions
B. BongiornoLuisa Di PiazzaKazimierz Musiałsubject
Pettis integralMathematics::Functional AnalysisPure mathematicssymbols.namesakeMeasurable functionGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsBanach spacesymbolsDisjoint setsLebesgue integrationMathematicsdescription
We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-01-01 |