Search results for "Radon-Nikodym Property"

showing 5 items of 5 documents

Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets

2013

We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that applies to these mappings and more generally to all almost everywhere metrically differentiable Lipschitz mappings defined on a Carnot group. peerReviewed

Discrete mathematicsMathematics::Functional AnalysisProperty (philosophy)General Mathematicsmetric area formulata111Mathematics::Analysis of PDEsCarnot groupBanach homogeneous groupsalmost everywhere differentiabilityRadon-Nikodym propertyLipschitz continuityRadon–Nikodym theoremBanach homogeneous groups; metric area formula; almost everywhere differentiability; Radon-Nikodym propertyMetric (mathematics)Homogeneous groupMathematics::Metric GeometryAlmost everywhereDifferentiable functionMathematics
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METRIC DIFFERENTIABILITY OF LIPSCHITZ MAPS

2013

AbstractAn extension of Rademacher’s theorem is proved for Lipschitz mappings between Banach spaces without the Radon–Nikodým property.

Mathematics::Functional AnalysisPure mathematicsGeneral MathematicsBanach spaceLipschitz continuityRadon-Nikodym PropertyLipschitz domainSettore MAT/05 - Analisi MatematicaLipschitz mapsMetric (mathematics)Metric mapMetric Diff erentiability.Differentiable functionMetric differentialSemi-differentiabilityMathematicsJournal of the Australian Mathematical Society
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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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RADEMACHER'S THEOREM IN BANACH SPACES WITHOUT RNP

2017

Abstract We improve a Duda’s theorem concerning metric and w *-Gâteaux differentiability of Lipschitz mappings, by replacing the σ-ideal 𝓐 of Aronszajn null sets [ARONSZAJN, N.: Differentiability of Lipschitzian mappings between Banach spaces, Studia Math. 57 (1976), 147–190], with the smaller σ-ideal 𝓐 of Preiss-Zajíček null sets [PREISS, D.—ZAJÍČEK, L.: Directional derivatives of Lipschitz functions, Israel J. Math. 125 (2001), 1–27]. We also prove the inclusion C̃ o ⊂ 𝓐, where C̃ o is the σ-ideal of Preiss null sets [PREISS, D.: Gâteaux differentiability of cone-monotone and pointwise Lipschitz functions, Israel J. Math. 203 (2014), 501–534].

Pure mathematicsRademacher's theoremSettore MAT/05 - Analisi MatematicaGeneral Mathematics010102 general mathematics0103 physical sciencesBanach spaceLipschitz maps Radon-Nikodym property metric Gateaux differentiability w-Gòateaux differentiability.010307 mathematical physics0101 mathematics01 natural sciencesMathematics
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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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