| 引用本文: | 金治明.非标准分析与概率论.[J].国防科技大学学报,1994,16(1):128-132.[点击复制] |
| Jin Zhiming.Non-Standard Analysis and Probability[J].Journal of National University of Defense Technology,1994,16(1):128-132[点击复制] |
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| 本文已被：浏览 5711次 下载 6467次 |
| 非标准分析与概率论 |
| 金治明 |
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(国防科技大学 系统工程与数学系 湖南 长沙 410073)
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| 摘要: |
| 本文概述了非标准分析发展的简史，介绍了超实数系，导数的非标准表示，并举例说明了数学命题的非标准证明比标准证明更为简洁、直观。文章的后一部分介绍了loeb概率空间以及概率积分的*有限求和的表示，并指出概率论从本质上是初等的结论。 |
| 关键词: 非标准分析，loeb 概率空间，* 有限求和 |
| DOI： |
| 投稿日期：1993-09-05 |
| 基金项目: |
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| Non-Standard Analysis and Probability |
| Jin Zhiming |
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(Department of Systems Engineering and Maths, NUDT, Changsha, 410073)
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| Abstract: |
| This paper gives a brief account of the history of non-standard analgsis and introduces the hyper-real system, the nonstandard representation of deriate. We illustrate that the proof of mathematical proposition by nonstandard methods is simpler and more directly perceived through the senses than standard methods. In the last part of the paper, we introduce the loeb probability space, the integral in respect to p as *-finite summation and point out that the probability theory is radically elementary. |
| Keywords: Non-standard analysis,loeb probability space,*-finite summation |
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