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

2021/11/16 by Lučić, Danka, Pasqualetto, Enrico · 1 citation
#18F15 #28A15 #28A50 #28A51 #46B22 #46G10 #46G15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2111.08526

Abstract

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-Nikodým property.

Cited by

• Tensor products of measurable Banach bundles

Related

• Differentiation of measures in metric spaces
• Uniform refinements, topological derivative and a differentiation theorem in metric spaces
• Rigidity of Derivations in the Plane and in Metric Measure Spaces
• Differentiation of measures on complete Riemannian manifolds
• Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon Nikodym property