关于可测函数5种常见定义的等价性

On the Definitions of Five Sorts of Ordinary Measurable Functions

在一维欧氏空间中列出了现今各种实变函数教材中有关可测函数的5种常见定义形式,并用初等方法证明了它们是相互等价的,揭示了可测函数这一概念的内涵,加深了对可测函数理论的理解,为以后应用可测函数打下了坚实的基础.

The definition forms of five sorts of ordinary measurable functions in all kinds of present teaching materials of real variable function were set out.They were proved equivalent to each other by elementary methods,revealing the notion of measurable functions connotations.The further understanding of the theory of measurable functions for the future application of measurable functions laid a solid foundation.