A GENERALIZATION OF THE DENSITY TOPOLOGY

被引：0
|
作者：
Wojdowski, Wojciech [1 ]
机构：
[1] Tech Univ Lodz, Inst Math, PL-90924 Lodz, Poland
来源：
REAL ANALYSIS EXCHANGE | 2006年 / 32卷 / 02期
关键词：
Density point; density topology;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Wilczynski's definition of the Lebesgue density point given in [W1] opened the possibility of more subtle properties of the notion of density point and the density topology, their various modifications and most of all category analogues. In this paper we introduce a notion of an A(d)-density point of a measurable set on the real line. The notion is a generalization of Lebesgue density and is based on the definition given by Wilczynski. We prove that the A(d)-density topology generated by this notion is strictly finer than the Lebesgue density topology and we examine several of its properties.
引用
收藏
页码：349 / 358
页数：10
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