摘要
实变函数是数学专业一门比较高深精细的理论课,也是公认的教师难教、学生难学的一门专业课,特别是对勒贝格测度及勒贝格积分的理解。那么如何使学生更容易掌握和理解测度、勒贝格积分的概念也是目前教学的一个挑战。文章以概率论中的古典概型和几何概型为基础,建立古典概型、几何概型与勒贝格测度、勒贝格积分之间的关系,并且通过具体实例说明概率问题测度化的过程,然后利用勒贝格积分解决一些概率问题,最后总结说明概率论在实变函数教学中的应用。
Real variable function is a more sophisticated theory for mathematics majors,and it is also recognized as a specialized course that is difficult for teachers to teach and students to learn,especially the understanding of Lebesgue measure and Lebesgue integral.So how to make it easier for students to grasp the concept of theoretical measure and Lebesgue integral is also a challenge for teaching at present.Based on the theory of probability in the classical schema and geometric model as the foundation,established the classical schema,geometric model and Lebesgue measure,the relationship between the Lebesgue integral,and through the concrete example is given to illustrate the process of measure of the probability problem,and then the probability of solving some problems using Lebesgue integral,finally summarized that the application of probability theory in real variable function teaching.
作者
郑前前
杨文杰
ZHENG Qianqian;YANG Wenjie(Xuchang University,School of Science,Xuchang,Henan 461000)
出处
《科教导刊》
2022年第8期123-125,共3页
The Guide Of Science & Education
基金
河南省科学技术协会-河南省青年人才托举工程项目(2020HYTP012)
河南省教育厅-河南省高校重点科研项目(21B130004)
许昌学院教研项目(XCU2019-ZZ-022)
许昌学院科研反哺教学项目(2020FB023)
关键词
实变函数
概率论
古典概型
几何概型
勒贝格
real variable function
probability theory
classical schema
geometric schema
Lebesgue
