关于容斥原理在勒贝格积分中的应用及推广  

Application and Generalization of Inclusion and Exclusion Principle in Lebesgue Integral

作　　者：唐大钊 雷桥[1] 

机构地区：[1]重庆师范大学数学学院,重庆401331

出　　处：《重庆工商大学学报（自然科学版）》2013年第12期7-10,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(11226633)

摘　　要：勒贝格积分作为黎曼积分的一种推广,它不仅大大扩充了可积函数的范围,而且对于研究函数的性质有着非常重要的作用;勒贝格积分中可测函数的一些性质,对于研究单个或者多个函数复合、加减也有及其重要的作用,在可测函数基本性质的基础上,将容斥原理推广到可测函数中,得出一系列相应的推论.Lebesgue integral, as a kind of generalization of Riemann integral, not only greatly expands the scope of integrable functions but also plays an important role in studying function property, and some properties of measurable functions in Lebesgue integral also play an important role in studying single or multiple function composition, addition and subtraction. On the basis of basic properties of measurable functions, this paper generalizes inclusion and exclusion principle into measurable functions and obtains a series of corresponding inferences.

关 键 词：容斥原理 可测函数 勒贝格积分 

分 类 号：O141[理学—数学]