Measure-category properties of Borel plane sets and Borel functions of two variables

被引：0
作者：
M. Balcerzak
S. Gła̧b
机构：
[1] Technical University of Łódź,Institute of Mathematics
来源：
Acta Mathematica Hungarica | 2010年 / 126卷
关键词：
Lebesgue measure; Baire category; Mendez ; -ideal; nice base of a ; -ideal; Nikodym’s theorem; Lusin’s theorem; 28A05; 26B05;
D O I：
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学科分类号：
摘要：
Let [graphic not available: see fulltext] stand for the Fubini-type product of σ-ideals [graphic not available: see fulltext]. We consider mixed measure-category σ-ideals [graphic not available: see fulltext] and [graphic not available: see fulltext] (called the Mendez σ-ideals), and study some features of their structure. We show that [graphic not available: see fulltext] and [graphic not available: see fulltext] are not invariant with respect to nonzero rotations. Using Fremlin’s results, we describe nice Borel bases of [graphic not available: see fulltext] and [graphic not available: see fulltext]. The rest of the paper is devoted to uniform versions of the Nikodym theorem and the Lusin theorem for Borel functions of two variables.
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页码：241 / 252
页数：11
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