The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
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.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Birkhäuser
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202303302345Use this for linking
Review status
Peer reviewed
ISSN
2662-2009
DOI
https://doi.org/10.1007/s43036-023-00258-w
Language
English
Published in
Advances in Operator Theory
Citation
- Lučić, D., & Pasqualetto, E. (2023). The metric-valued Lebesgue differentiation theorem in measure spaces and its applications. Advances in Operator Theory, 8(2), Article 32. https://doi.org/10.1007/s43036-023-00258-w
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
Open Access funding provided by University of Jyväskylä (JYU). The first named author acknowledges the support by the project 2017TEXA3H “Gradient flows, Optimal Transport and Metric Measure Structures”, funded by the Italian Ministry of Research and University. The second named author acknowledges the support by the Balzan project led by Luigi Ambrosio. Both authors acknowledge the support by the Academy of Finland, Grant no. 314789
Copyright© The Author(s) 2023