中文摘要：

从可测函数与连续函数的关系出发,利用Lebesgue积分理论与R-S积分的性质,把积分第二中值定理的条件从R可积推广到L可积,并给出了一个新的简洁证明.

英文摘要：

This paper, within the theory of the Lebesgue integration and R-S integration, extended the condition of the second integral mean value theorem from Riemann integration to Lebesgue integration. Furthermore, from the relationship between the measurable function and continuous function, a brief proof of the extended one is obtained.