浅析集合分析法在实变函数中的应用

Application of the set analysis method in real variable functions

集合分析法是使用集合运算的语言来描述函数列在可测集上的极限过程,是实变函数的主要分析方法之一,在叶果洛夫定理、黎斯定理、Lebesgue控制收敛定理等这些定理的证明中常常用到,通过三道典型的题目探讨该方法在实变函数中的应用。

The set analysis method is a method which denotes the limit of a sequence of functions on measurable sets by set operations. It is one of the main analysis methods in real variable functions, and is often used in the proofs of theorems, such as, the Eropob Theorem, the Riesz Theorem and the Lebesgue Dominated Convergence Theorem. In this paper, through three classical examples, we discuss the applications of this method in real variable functions.