刍议实变函数课的'承上启下'作用

摘要

The curriculum of functions of a real variable is the class of the connecting link between the preceding and the following. One aspect, it is continual naturally in mathematical analysis, so it is necessary to compare the main concept of the functions of a real variable with the corresponding part concept of mathematical analysis. Another aspect, it is the basic of probability theory, measure theory, random process, therefore, it is necessary to carry out the appropriate abstract, extending at the end of the course to lay down basis.%实变函数课是一门"承上启下"的课.一方面,它是数学分析课的自然延续,因此有必要把实变函数中主要概念与数学分析中相应部分进行比较.另一方面,它又是概率论、测度论、随机过程等课程的基础,因此有必要在课程结束时进行适当的抽象、延伸,为后继课程的学习打下基础.