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

被引：2
|
作者：
Lucic, Danka [1 ]
Pasqualetto, Enrico [1 ]
机构：
[1] Univ Jyvaskyla, Dept Math & Stat, POB MaD 35, Box 35 MaD, Jyvaskyla 40014, Finland
来源：
ADVANCES IN OPERATOR THEORY | 2023年 / 8卷 / 02期
基金：
芬兰科学院;
关键词：
Lebesgue differentiation theorem; von Neumann lifting; Measurable Banach bundle; Radon-NikodATIN SMALL LETTER Y WITH ACUTEm property; Disintegration of a measure; LIFTINGS;
D O I：
10.1007/s43036-023-00258-w
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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-NikodATIN SMALL LETTER Y WITH ACUTEm property.
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页数：51
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