| 因果空间和概率论中集合论方法 |
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| 引用本文： | 熊大国.因果空间和概率论中集合论方法[J].北京理工大学学报,2005,25(1):31-34. |
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| 作者姓名： | 熊大国 |
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| 作者单位： | 北京理工大学,信息科学技术学院自动控制系,北京,100081 |
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| 摘 要： | 建立<概率论自然公理系统>中的第Ⅰ组和第Ⅱ组公理.这两组公理把随机世界抽象成既直观又形象的因果空间.在因果空间中随机事件是原因点的集合,原因点的伪出现导致事件的出现.证明概率论中集合论方法是因果空间的产物,从而改变了Kolmogorov公理系统把集合论方法硬性地搬到概率论中的做法.
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| 关 键 词： | 公理系统 因果空间 事件空间 原因空间 原因点 |
| 文章编号： | 1001-0645(2005)01-0031-04 |
| 收稿时间： | 2004/11/1 0:00:00 |
| 修稿时间： | 2004年11月1日 |
Causation Space and the Set Methodology in Probability Theory |
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| XIONG Da-guo.Causation Space and the Set Methodology in Probability Theory[J].Journal of Beijing Institute of Technology(Natural Science Edition),2005,25(1):31-34. |
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| Authors: | XIONG Da-guo |
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| Institution: | Department of Automatic Control, School of Information Science and Technology, Beijing Institute of Technology, Beijing100081, China |
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| Abstract: | Two groups of axioms in the natural axiom system of probability theory are set up. By the help of them the random universe will be abstracted into a causation space which is more intuitional and figurative. In the causation space, a random event is a set of cause points and the pseudo-occurence of a cause point will induce the occurence of some events. Theorem 2 proves that the set methodology in probability theory is the product of the causation space, and in this way the practice of indiscriminatingly applying the set methodology into probability theory by Kolmogorov's axiom system can be avoided. |
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| Keywords: | axiom system causation space event space cause space cause point |
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