黎曼积分和勒贝格积分的比较

The Comparison of Riemann Integral and Lebesgue Integral

黎曼积分和勒贝格积分之间有一种相互依赖、相互补充、相互帮助及在特定条件下相互转化的关系。本文主要通过对两类积分存在条件、基本性质、可积函数类以及相关结论的分析,结合具体实例比较黎曼积分与勒贝格积分,以期得到二者的区别与联系。

There is an interdependent, mutually complementary, mutually helping relation and mutually transformational relation- ship under the specific conditions between the Riemann integral and the Lebesgue integral. This paper mainly analyzes the exis- tent conditions, basic natures, the class of integrable function and the relevant conclusions, and compares the Riemann integral and the Lebesgue integral with the specific examples, aiming to get the difference and connection between them.