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

Danka LučićEnrico Pasqualetto

subject

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)

description

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.

yearjournalcountryeditionlanguage
2021-11-16
http://arxiv.org/abs/2111.08526