The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
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
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Advances in Operator TheoryDate
2023Copyright
© The Author(s) 2023
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.
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BirkhäuserISSN Search the Publication Forum
2662-2009Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/182530148
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Academy Project, AoFAdditional 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 t ...
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