关于和函数分析性质的几个问题的讨论

A Discussion on Problems of Analytical Properties of Sum Function

通过反例说明了一致收敛是和函数分析性质的充分而非必要条件,由此看出在数学分析教学中合理恰当地运用反例会收到很好的教学效果;同时给出和函数连续性的三种等价形式,而且在使用时,各有好处,最后给出判断一个函数项级数非一致收敛的判别法.

This paper shows with inverse examples that consistence convergence is a full but notnecessary condition for analytical properties of sum function, which sees good effect on teachingmathematics if used properly. Meanwhile three equavilencies for sum function consistency, andthe advantages in use, is provided. In the last part, the way to judge a nonconsistence convergence of the number of a fuction term grade.