“一致收敛”概念的推广及其应用

The Spreading and Application of the Concept "Uniform Convergence"

本文通过引入函数项级数和含参变量广义积分次一致收敛的概念,证明了函数项级数的和函数、含参变量广义积分连续性的充要条件以及可积性、可微性的充分条件,推广了数学分析中一致收敛的概念以及相应结论。

Through introduction of the concepts of series with function terms and uniform convergence with generalized integral time parameter, this paper proves the necessary and sufficient conditions of series with function terms and the generalized integral continuity parameter as well as the necessary and sufficient conditions of integra- bility and differentiability, spreads the concept of uniform convergence in mathematics analysis and the corresponding conclusions.