可积函数的逼近性质的证明及其应用

The Proof and Application to Integrable Function Approximation Quality

考虑黎曼可积函数可用阶梯函数和连续函数逼近的问题,应用黎曼可积函数的充分必要条件定理,给出了可积函数的逼近结果的详细证明,并指出了这些逼近结果的一些应用,沟通了相关问题之间的联系和发展变化.

In this paper, we consider a question that Riemann integrable function can be approached by continuous function and step function. According to necessary and sufficient condition of Riemann integrable function, give detailed proof of the integrable function approximation. In addition, we point out some applications to the results of the approximation and communicate the link among these relative questions.