实变函数反例研究(Ⅰ)  

Study on the Counterexamples in Function of Real Variable(Ⅰ)

作　　者：范洪福[1] 范子杰[2] FAN Hong-fu;FAN Zi-jie(College of Science,University of Shanghai for Science&Technology,Shanghai 200093,China;Department of Customs Management,Shanghai Customs College,Shanghai 201204,China)

机构地区：[1]上海理工大学理学院,上海200093 [2]上海海关学院海关管理系,上海201204

出　　处：《大学数学》2018年第6期52-55,共4页College Mathematics

摘　　要：在一般测度积分(非Lebesgue测度与积分)的框架下构造了实变函数中的多个反例.它们说明不同概念之间的区别,以及一些常用结论在缺乏相应的条件之后不再成立.这有力地补充了教材[1].In the framework of general measure integral(non-Lebesgue measure and integral),several counterexamples in function of real variable are constructed.They show the differences between different concepts,and some common conclusions would no longer be tenable in the absence of corresponding conditions.This strongly complements the textbook[1].

关 键 词：代数与σ代数 测度空间 LEBESGUE定理 RIESZ定理 反例 

分 类 号：O174.1[理学—数学]