徐利治,孙广润.关于Poincaré氏注记和定义在*(Rn)上的一种非标准测度[J].数学研究及应用,2001,21(2):159~164
关于Poincaré氏注记和定义在*(Rn)上的一种非标准测度
On Poincaré′s Remark and a Kind ofNonstandard Measure Defined on *(Rn)
投稿时间:2000-12-02  
DOI:10.3770/j.issn:1000-341X.2001.02.001
中文关键词:  
英文关键词:Poincaré's remark  Cantor's continuum  enlargement  hyperfinite set  hyperstandard measure.
基金项目:
作者单位
徐利治 大连理工大学应用数学系辽宁 116024 
孙广润 曲阜师范大学数学系山东 273165 
摘要点击次数: 2647
全文下载次数: 1605
中文摘要:
      受到Poincaré氏评注的启发,本文引入了一种新的非标准测度,简称为μh测度.文中应用非标准分析方法证明了标准实数集R在*R上的μh测度为零.文末还指出了μh测度与Lebesgue测度具有相异本质的原由.
英文摘要:
      Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space *(Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of real numbers is of measure zero. The proposition just mentioned is basically consistent with Poincaré's famous remark which renders a deep insight into the paradoxical structural nature of Cantor's continuum consisting precisely of all distinct real numbers.
查看全文  查看/发表评论  下载PDF阅读器