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

被引：0
|
作者：
Danka Lučić
Enrico Pasqualetto
机构：
[1] University of Jyvaskyla,Department of Mathematics and Statistics
来源：
Advances in Operator Theory | 2023年 / 8卷
关键词：
Lebesgue differentiation theorem; von Neumann lifting; Measurable Banach bundle; Radon–Nikodým property; Disintegration of a measure; 28A15; 28A51; 46G15; 18F15; 46G10; 46B22; 28A50;
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学科分类号：
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–Nikodým property.
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