Lebesgue积分几何意义的推广  

A Generalization of the Geometric Significance of Lebesgue Integral

作　　者：顾华飞[1] 王明治[1] 

机构地区：[1]湖州师范学院数学系,浙江湖州313000

出　　处：《数学的实践与认识》2011年第23期236-241,共6页Mathematics in Practice and Theory

基　　金：<复变函数>国家精品课程项目;国家特色专业建设点和浙江省新世纪教改项目(yb07109)

摘　　要：证明了非负有界函数的Lebesgue上积分等于函数下方图形的Lebesgue外测度,其Lebesgue下积分等于函数下方图形的Lebesgue内测度,从而将积分的几何意义从可测情形推广到一般情形.In this article we prove that the Lebesgue upper integral of a bounded non- negative function is the Lebesgue outer measure of the graph below the function, and the Lebesgue lower integral is the Lebesgue inner measure of the graph below the function. Thus, the geometric significance of the integral can be extended from the measurable case to general cases.

关 键 词：内测度 外测度 上积分 下积分 

分 类 号：O172.2[理学—数学]