6533b85bfe1ef96bd12ba0de
RESEARCH PRODUCT
A decomposition theorem for compact-valued Henstock integral
L. Di PiazzaKazimierz Musiałsubject
Discrete mathematicsIntegrable systemSelection (relational algebra)MultifunctionHenstock integralIf and only ifGeneral MathematicsBanach spacePettis integralKurzweil–Henstock–Pettis integral selectionSeparable spaceMathematicsDecomposition theoremdescription
We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-02-20 |