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

Lučić, Danka; Pasqualetto, Enrico

doi:10.1007/s43036-023-00258-w

dc.contributor.author	Lučić, Danka
dc.contributor.author	Pasqualetto, Enrico
dc.date.accessioned	2023-03-30T11:23:26Z
dc.date.available	2023-03-30T11:23:26Z
dc.date.issued	2023
dc.identifier.citation	Lučić, D., & Pasqualetto, E. (2023). The metric-valued Lebesgue differentiation theorem in measure spaces and its applications. <i>Advances in Operator Theory</i>, <i>8</i>(2), Article 32. <a href="https://doi.org/10.1007/s43036-023-00258-w" target="_blank">https://doi.org/10.1007/s43036-023-00258-w</a>
dc.identifier.other	CONVID_182530148
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/86210
dc.description.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.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Birkhäuser
dc.relation.ispartofseries	Advances in Operator Theory
dc.rights	CC BY 4.0
dc.subject.other	Lebesgue differentiation theorem
dc.subject.other	von Neumann lifting
dc.subject.other	measurable Banach bundle
dc.subject.other	Radon–Nikodým property
dc.subject.other	disintegration of a measure
dc.title	The metric-valued Lebesgue differentiation theorem in measure spaces and its applications
dc.type	research article
dc.identifier.urn	URN:NBN:fi:jyu-202303302345
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.relation.issn	2662-2009
dc.relation.numberinseries	2
dc.relation.volume	8
dc.type.version	publishedVersion
dc.rights.copyright	© The Author(s) 2023
dc.rights.accesslevel	openAccess	fi
dc.type.publication	article
dc.relation.grantnumber	314789
dc.subject.yso	Banachin avaruudet
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p38972
dc.rights.url	https://creativecommons.org/licenses/by/4.0/
dc.relation.doi	10.1007/s43036-023-00258-w
dc.relation.funder	Research Council of Finland	en
dc.relation.funder	Suomen Akatemia	fi
jyx.fundingprogram	Academy Project, AoF	en
jyx.fundingprogram	Akatemiahanke, SA	fi
jyx.fundinginformation	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
dc.type.okm	A1