实变函数中简单函数的研究  

The Application of Simple Functions in Real Variable Functions

作　　者：李晓萌[1] 秦喜梅[1] 苏先锋 LI Xiao-meng;QIN Xi-mei;SU Xian-feng(School of Mathematics and Big Data,Chaohu University,230000,Hefei Anhui,China;School of Mathematical Science,Huaibei Normal University,235000,Huaibei Anhui,China)

机构地区：[1]巢湖学院数学与大数据学院,安徽合肥230000 [2]淮北师范大学数学科学学院,安徽淮北235000

出　　处：《河北北方学院学报（自然科学版）》2024年第5期1-5,共5页Journal of Hebei North University:Natural Science Edition

基　　金：安徽省教育厅重大教研项目《OBE理念下应用型本科高校教学质量持续改进机制构建与实践》(2022jcbs037);安徽省教育厅教学研究重点项目《课程思政融入高等数学教学的研究》(2020jyxm1697);巢湖学院数学重点建设学科项目(kj22zdjsxk01)。

摘　　要：实变函数较之数学分析更加抽象复杂,是近代数学的重要基础。简单函数是实变函数中非常基础且具体的重要函数类。围绕简单函数与可测函数间的联系,及其在Lebesgue积分中的运用等问题开展研究,探讨简单函数在实变函数教学中的广泛应用,以期实现降低学习的难度提升实变函数的教学效果目的。and complex than mathematical analysis and is an important foundation of modern mathematics.Simple function is a very basic and concrete function class in real variable function.Therefore,this paper will focus on the relationship between simple function and measurable function,and its application in Lebesgue integral,so as to explore the wide application of simple function in the teaching of real variable function,in order to achieve the purpose of reducing the difficulty of learning and improving the teaching effect of real variable function.

关 键 词：实变函数 简单函数 LEBESGUE测度 LEBESGUE积分 

分 类 号：O174[理学—数学]