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
Published in
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.
Publisher
BirkhäuserISSN Search the Publication Forum
2662-2009Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/182530148
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
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 the Academy of Finland, Grant no. 314789 ...License
Related items
Showing items with similar title or keywords.
-
Radon–Nikodym Property and Area Formula for Banach Homogeneous Group Targets
Magnani, Valentino; Rajala, Tapio (Oxford University Press, 2014)We prove a Rademacher-type theorem for Lipschitz mappings from a subset of a Carnot group to a Banach homogeneous group, equipped with a suitably weakened Radon-Nikodym property. We provide a metric area formula that ... -
On the reflexivity properties of Banach bundles and Banach modules
Lučić, Milica; Pasqualetto, Enrico; Vojnović, Ivana (Birkhäuser, 2024)In this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a σ-finite measure space. Our two main results are the following: • The fibers of a bundle are uniformly convex ... -
Failure of Topological Rigidity Results for the Measure Contraction Property
Ketterer, Christian; Rajala, Tapio (Springer Netherlands, 2015)We give two examples of metric measure spaces satisfying the measure contraction property MCP(K, N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0, 3) and ... -
On Decoupling in Banach Spaces
Cox, Sonja; Geiss, Stefan (Springer, 2021)We consider decoupling inequalities for random variables taking values in a Banach space X. We restrict the class of distributions that appear as conditional distributions while decoupling and show that each adapted process ... -
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
Le Donne, Enrico; Rajala, Tapio; Walsberg, Erik (American Mathematical Society, 2018)We consider a general notion of snowflake of a metric space by composing the distance with a nontrivial concave function. We prove that a snowflake of a metric space X isometrically embeds into some finite-dimensional ...