函数可积性的进一步讨论

Further Discussion of Function Integrability

本文首先介绍了可积函数的概念;其次介绍了函数可积性的充分、必要和充分必要条件。重点研究一元函数可积性的反例的构造。最后结合例子进一步讨论了如何证明一个函数在给定区间上是否可积的问题,例如:复合函数的可积性。

Firstly, we introduce the concept of integrable function in the paper;secondly, the sufficient condi-tion, necessary condition, sufficient and necessary condition of the integrability of function are in-troduced. We mainly focus on the counter-example construction of integrability of one variable function. Finally, combining with examples, we further discuss the problem that how to prove whether a function is integrable on a given interval, for example: the integrability of the composite function.