导数新定义间相互关系的进一步研究

The further research of the new defining of the derivative and their relation

文章继文 [1 ]进一步讨论了导数新定义间相互联系 ,特别当 f ( x)为 U( x0 )内有界可测函数的条件下 ,证明了定义 5真包含定义 2 ,并由引理给出了 Riemann上、下积分与 Lebesgue积分之间的关系 .

In this paper the author gives the relation between defining 5 and defining 2 of the derivative, which is studied in [1]by Lu. The relation is that if f: R→R is a measurable and bounded funcation in U(x 0) , the neighbour of x 0 , the defining 5 generalizes defining 2 ferthermore, the author give out the relation between the up(down)-Riemann integral and the Lebesgue integral.