摘要
函数列的收敛性不一定导致它的一致收敛性.然而对于特殊的函数列可证明命题成立.本文利用凸函数的特性,证明收敛的凸函数列的一致收敛性.
For a sequence of arbitrary functions, uniform convergence can't be implied by pointwise convergence. But for the sequence of particalar functions, such as sequence of convex functions, uniform convergence can be implied by pointwise convergence . In this paper , the claim bollows from the properties of convex functions .
关键词
凸函数
一致收敛
函数列
convex functions
uniform convergence
