Search results for " variational measure"

showing 4 items of 4 documents

A variational henstock integral characterization of the radon-nikodým property

2009

A characterization of Banach spaces possessing the Radon-Nikodym property is given in terms of finitely additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an X-valued function. Due to that characterization several X-valued set functions that are only finitely additive can be represented as integrals.

Settore MAT/05 - Analisi MatematicaHenstock integral Pettis integral variational measure Radon-Nikodym property
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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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Differentiation of an additive interval measure with values in a conjugate Banach space

2014

We present a complete characterization of finitely additive interval measures with values in conjugate Banach spaces which can be represented as Henstock-Kurzweil-Gelfand integrals. If the range space has the weak Radon-Nikodým property (WRNP), then we precisely describe when these integrals are in fact Henstock-Kurzweil-Pettis integrals.

Pettis integralMathematics::Functional AnalysisPure mathematics54C60General MathematicsMathematical analysisMathematics::Classical Analysis and ODEsBanach spacevariational measureKurzweil-Henstock integralCharacterization (mathematics)Space (mathematics)Measure (mathematics)Kurzweil--Henstock integral Pettis integral variational measure.28B05Range (mathematics)26A39Settore MAT/05 - Analisi MatematicaPettis integral28B20Interval (graph theory)46G10MathematicsConjugate
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Variational measures related to local systems and the Ward propery of P-adic path bases

2006

Some properties of absolutely continuous variational measures associated with local systems of sets are established. The classes of functions generating such measures are described. It is shown by constructing an example that there exists a P-adic path system that defines a differentiation basis which does not possess Ward property.

Local system P-adic system differentiation basis variational measure Ward property.
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