Calculus of Variations and Geometric Measure Theory
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D. Lučić - E. Pasqualetto

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

created by lučić on 17 Nov 2021

[BibTeX]

preprint

Inserted: 17 nov 2021
Last Updated: 17 nov 2021

Year: 2021

ArXiv: 2111.08526 PDF

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-Nikodym property.

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