《实变函数与泛函分析》课程改革——一维化方法和测度论,可测函数和积分论学习路径

Reform in the Course Real and Functional Analysis——One Dimensional Method and the Study Roadmap for Measure Theory,Measurable Functions and Integration Theory

本文探讨了《实变函数与泛函分析》课程内容改革,一是采用一维化方法从一维实数空间的测度论开始学习,二是采用测度的可数可加性圯叶戈洛夫定理圯有界收敛定理的学习路径学习测度论,可测函数和积分论的性质。此教学方案突出课程核心内容,减轻了课程难度,适合数学类和相关专业学生学习。

The paper discusses the reform of the course Real and Functional Analysis.Firstly,we adopt the one dimensional method to study the measure theory,secondly,we adopt the study roadmap,the countable additivity of measure=>Egoroff’s Theorem=>Bounded Convergence Theorem,to study the measure theory,measurable functions and integration theory.The course plan emphasizes the core contents of the course and alleviates the study difficulty,thus the course is suitable for the students majoring in mathematics and related fields.