复合函数的勒贝格可积性研究

Study of Lebesgue integrability of composite function

复合函数的勒贝格可积性质在几何学、物理,以及数学分析、实变函数等学科中都有着十分重要的作用.本文以函数勒贝格可积的定义为出发点,通过收集整理相关资料,指出和证明了函数勒贝格可积和复合函数勒贝格可积的几个条件,以及可测函数的结构等结论,并给出了应用.

The Lebesgue integrability of composite function plays an important role in geometry, physics, and mathematical analysis, real variable and other disciplines. In this paper, Lebesgue integrable function is defined as the starting point. Through collecting and collating relevant information and proof, several conditions of the function Lebesgue integrable and Lebesgue integrable complex function were pointed out and proved, as well as the structure of measurable functions and so on, and the applications were given.