Abstract: In the paper, the proof of R．一N．theorem is discussed by using Riesz·Banach theorem．The proof of the theorem in[I]is improved．There are two methods of proof on R．·N．theorem ．which have diferent ways and it is worth to research

Key words: R—N．theorem, measure, linear subspace, absolute continue

摘要： 笔者在本文讨论应用Riesz-Frechet定理证明R-N定理。拟定的证明改进了文[1]中给出的简略证明，且在 问题的处理方面与文[1]的论述略有不同。R-N定理的两种证明方式各有其独特之处。这两种证法都值得研究

关键词: R-N定理, 测度, 有界线性泛函, 线性子空间, 绝对连续