| 关于Poincaré氏注记和定义在*(Rn)上的一种非标准测度 |
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| 引用本文： | 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. |
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| 作者姓名： | 徐利治 孙广润 |
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| 作者单位： | 大连理工大学应用数学系，辽宁 116024;曲阜师范大学数学系，山东 273165 |
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| 基金项目： | Supported by Special
Foundation of Dalian Univ. of Technology. |
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| 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.
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| 关 键 词： | Poincaré's remark Cantor's continuum enlargement hyperfinite set hyperstandard measure. |
| 文章编号： | 1000-341X(2001)02-0159-06 |
| 收稿时间： | 2000/12/2 0:00:00 |
| 修稿时间： | 2000年12月2日 |
On Poincar |
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| L. C. Hsu and SUN Guang-run.On Poincar[J].Journal of Mathematical Research with Applications,2001,21(2):159-164. |
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| Authors: | L C Hsu and SUN Guang-run |
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| Institution: | Dept. of Math., Dalian University of Technology, 116024, China;Dept. of Math., Qufu Normal University, Shandong 273165, China |
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| Abstract: | 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. |
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