G积分的性质

The Properties of the G integrable function

Botsko在连续和可导的知识基础推广了Riemann积分,得到了一种新的积分,称为G积分.文[1]研究了G可积函数的Lebesgue可测性.本文研究了G积分的逐项积分、两个函数的积的G积分以及G积分的中值定理等一系列问题,并给出了一个G可积Riemann不可积的有界函数的例子.

M.W. Botsko, based on the concepts of continuity and the derivative, generalized the Riemann integral and obtained a new integral-G integral. In paper[ 1 ], the authors studied the Lebesgue measurability of the Gintegrable function. And in this paper,the author study the series of integration term by term of the G integral, the G integral of two functions＇ product and the mean value theory of the G integra. At the same time, the author puts forward a bounded function which is not Riemann integrable but G integrable.