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, Article 32. https://doi.org/10.1007/s43036-023-00258-w
Published inAdvances in Operator Theory
© 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.
ISSN Search the Publication Forum2662-2009
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingOpen 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 ...
Showing items with similar title or keywords.
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 ...
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 ...
Baum-Katz’s Type Theorems for Pairwise Independent Random Elements in Certain Metric Spaces Nguyen, Tran Thuan; Quang, Nguyen Van (National Center for Scientific Research, 2020)In this study, some Baum-Katz’s type theorems for pairwise independent random elements are extended to a metric space endowed with a convex combination operation. Our results are considered in the cases of identically ...
The Choquet and Kellogg properties for the fine topology when p=1 in metric spaces Lahti, Panu (Elsevier Masson, 2019)In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar´e inequality, we prove the fine Kellogg property, the quasi-Lindel¨of principle, and the Choquet property for the ...
A new Cartan-type property and strict quasicoverings when P = 1 in metric spaces Lahti, Panu (Suomalainen tiedeakatemia, 2018)In a complete metric space that is equipped with a doubling measure and supports a Poincaré inequality, we prove a new Cartan-type property for the fine topology in the case p = 1. Then we use this property to prove the ...