摘要
Ｐ．Ｎａｌｉ和Ｇ．Ａｎｄｒｅｏｌｉ曾发表了关于黎曼·斯帝阶斯积分的存在条件，陈建功和严绍宗在一篇论文中指出该条件的充分性的原证有误，并给出了一个严格的证明，但证明较繁杂．
In 1929, P. Nalli and G. Andreoli gave a condition necessary and sufficient for the existence of integral (RS)∫ b af(x)dα(x) where f(x) is bounded in and α(x) is of bounded variation in . But the original proof of the sufficiency part of the theorem is invalid. In 1959, Chen Jiangong and Yan Shaozong gave a strict proof of the sufficiency part. But their proof is rather long. In this paper we gave a very short proof of the sufficiency part.
关键词
黎曼-斯帝阶斯
积分
有界变差函数
存在条件
Riemann Rtieltjes integral\ function of bounded variation total variation\ positive variation\ negative variation
