中文摘要：

研究了光滑收敛函数序列的极限函数不可积的存在性.运用稠密性论证、函数光滑化技术、胖康托集的构造技术,结合函数的平移特性和黎曼可积的勒贝格准则,获得了一列有界的光滑收敛函数序列,其极限函数在黎曼积分意义下不可积,并给出构造极限函数不可积的一般方法.

英文摘要：

The existence of the non-integrable limit of smooth function series was obtained in this study by combining dense argumentation and regularization by convolution, construction of fat Cantor-type set with functional translation and Lebesgue′s criterion for Riemann integra-bility, and the limit of some smooth functions is proved to be Riemann non-integrable. Some approaches to the construction of the Riemann non-integrable limit function are presented.