丁韫， 杨晓春^*

（  大连海事大学数学系；  ）

摘要： 本文主要从Riemann积分和Lebesgue 积分的定义出发，通过对讨论这两种积分的约定、初衷和目的比较和分析，探讨了这两种积分之间发生继承和变异的具体原因，提出了人们在认识积分中应该注意的一些问题。文中将这些问题分成了几个层次，逐一比较，这种比较不仅仅是局限于外表，而注重与发掘出隐藏于这些外表下的原因，并得到具体的结论。
关键词： Riemann积分；Lebesgue 积分；可积性；继承与变异.

DING Yun， YANG Xiaochun^*

（  Mathematics Department of Dalian Maritime University；  ）

Abstract： Abstract Based on definitions of Riemann integral and Lebesgue integral, the paper gives the comparison and analysis of the agreement, original intension and purpose of them to discuss the specific reason of the inheritance and variation between these two kinds of integrals. Accordingly the paper put forward some problems to which one should pay more attention when learning integrals. In comparison and analysis, we divide these problems into several levels and compare them one by one. And the comparison is not only restricted to superficial but to dig more meaningful reasons under it and then to draw some specific conclusions.

Tag：

点此返回栏目查看更多>>>参考论文