Search results for "Radon–Nikodým property"

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The metric-valued Lebesgue differentiation theorem in measure spaces and its applications

2021

We prove a version of the Lebesgue Differentiation Theorem for mappings that are defined on a measure space and take values into a metric space, with respect to the differentiation basis induced by a von Neumann lifting. As a consequence, we obtain a lifting theorem for the space of sections of a measurable Banach bundle and a disintegration theorem for vector measures whose target is a Banach space with the Radon-Nikod\'{y}m property.

Mathematics - Functional AnalysisMathematics::Functional AnalysisAlgebra and Number Theorymeasurable Banach bundleLebesgue differentiation theoremFOS: MathematicsRadon–Nikodým propertyBanachin avaruudetdisintegration of a measure28A15 28A51 46G15 18F15 46G10 46B22 28A50von Neumann liftingAnalysisFunctional Analysis (math.FA)
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Operator martingale decomposition and the Radon-Nikodym property in Banach spaces

2010

Abstract We consider submartingales and uniform amarts of maps acting between a Banach lattice and a Banach lattice or a Banach space. In this measure-free setting of martingale theory, it is known that a Banach space Y has the Radon–Nikodým property if and only if every uniformly norm bounded martingale defined on the Chaney–Schaefer l-tensor product E ⊗ ˜ l Y , where E is a suitable Banach lattice, is norm convergent. We present applications of this result. Firstly, an analogues characterization for Banach lattices Y with the Radon–Nikodým property is given in terms of a suitable set of submartingales (supermartingales) on E ⊗ ˜ l Y . Secondly, we derive a Riesz decomposition for uniform …

Uniform amartPure mathematicsDinculeanu operatorApproximation propertyEberlein–Šmulian theoremBanach spaceRadon–Nikodým propertyFinite-rank operatorBanach manifoldBanach lattice Banach space Bochner norm Cone absolutely summing operator Convergent martingale Convergent submartingale Dinculeanu operator Radon–Nikodým propertySettore MAT/05 - Analisi MatematicaLp spaceC0-semigroupBanach lattice Banach space Bochner norm Cone absolutely summing operator Convergent martingale Convergent submartingale Dinculeanu operator Radon–Nikodým property Uniform amartMathematicsDiscrete mathematicsMathematics::Functional AnalysisBanach spaceApplied MathematicsConvergent martingaleConvergent submartingaleBanach latticeBochner normCone absolutely summing operatorBounded functionAnalysis
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