Search results for "Kurzweil–Henstock–Pettis integral"

showing 2 items of 2 documents

A decomposition theorem for compact-valued Henstock integral

2006

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.

Discrete mathematicsIntegrable systemSelection (relational algebra)MultifunctionHenstock integralIf and only ifGeneral MathematicsBanach spacePettis integralKurzweil–Henstock–Pettis integral selectionSeparable spaceMathematicsDecomposition theorem
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Set valued Kurzweil-Henstock-Pettis integral

2005

It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.

Pettis integralKurzweil–Henstock integralMathematics::Functional AnalysisPure mathematicsGeneralizationApplied MathematicsMathematical analysisKurzweil–Henstock–Pettis integralMathematics::Classical Analysis and ODEsRegular polygonselectionRiemann–Stieltjes integralRiemann integralSupport functionLebesgue integrationsupport functionsymbols.namesakemultifunctionPettis set-valued integralsymbolsMathematics::Metric GeometryDaniell integralAnalysisMathematics
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