0000000000649988

AUTHOR

K. Musiał

showing 3 related works from this author

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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A CHARACTERIZATION OF THE WEAK RADON–NIKODÝM PROPERTY BY FINITELY ADDITIVE INTERVAL FUNCTIONS

2009

AbstractA characterization of Banach spaces possessing the weak Radon–Nikodým property is given in terms of finitely additive interval functions. Due to that characterization several Banach space valued set functions that are only finitely additive can be represented as integrals.

Pettis integralDiscrete mathematicsMathematics::Functional AnalysisPure mathematicsKurzweil-Henstock integral Pettis integral variational measure weak Radon-Nikodym property.Property (philosophy)General MathematicsBanach spacechemistry.chemical_elementRadonInterval (mathematics)Characterization (mathematics)chemistrySettore MAT/05 - Analisi MatematicaSet functionMathematicsBulletin of the Australian Mathematical Society
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APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS

2008

AbstractThe approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.

Sobolev spacePure mathematicsRelatively compact subspaceIntegrable systemGeneral MathematicsNorm (mathematics)Step functionMathematical analysisBounded variationBanach spaceLocally integrable functionMathematicsGlasgow Mathematical Journal
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