区间上的单调函数的连续性及其广义反函数  

Continuity of Monotone Function on Interval and It’s Generalized Inverse Function

作　　者：冯海亮 亓洪胜 宋萌萌 FENG Hai-liang;QI Hong-sheng;SONG Meng-meng(School of Mathematics and Physics,Bengbu University,Bengbu,233030,Anhui)

机构地区：[1]蚌埠学院数理学院,安徽蚌埠233030

出　　处：《蚌埠学院学报》2023年第2期103-105,共3页Journal of Bengbu University

基　　金：安徽高校自然科学重点项目(KJ2020A0751);安徽省大学生创新创业项目(S202011305053)。

摘　　要：利用勒贝格测度理论证明了区间上的单调函数几乎处处连续,利用商集理论定义了一种带有参数的广义反函数,证明其与原函数具有相同的单调性。在此基础上,证明了广义反函数的广义反函数几乎处处等于原函数,并给出了实例加以印证。The monotone function on the interval is almost continuous everywhere,which was obtained by using the theory of Lebesgue measure in this paper.The concept of generalized inverse function with parameters was defined by using quotient set theory,and it was proved to have the same monotonicity as the original function.The theory that the generalized inverse function of the generalized inverse function is almost always equal to the original function is proved,and an example has been given at last.

关 键 词：单调函数 勒贝格测度 几乎处处连续 商集 广义反函数 

分 类 号：O174.1[理学—数学]