函数序列一致收敛性的分析与证明

Analysis and proof methods of convergence uniform for functions sequence

函数序列一致收敛性是数学专业微积分理论特有的教学内容,既是重点也是难点,着重围绕着"有限支点法",对一致收敛性证明中常用的工具:有限覆盖定理,致密性原理,单调性,一致连续性,李普希兹条件的应用技巧进行了分析与探讨.

The convergence uniform for functions sequence is the peculiar content of the calculus for the students of mathematics specialty. It is both the key point also is the difficult point. In this paper,we mainly consider the finite supporting point methods and discuss the applications of the theorem of finite covering,accumulation principle,monotonicity,uniform continuity and Lipschitz condition.