非标准分析与概率论

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。

Non-Standard Analysis and Probability

This paper qives 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 infroduce the loeb probability space, the integral in respect to p as *-finite summation and point out that the probability theory is radically elementary