众所周知，连续函数列的极限函数不一定是连续的，这在理论与应用上均造成许多障碍。
The limit function of the sequence of continous function is not always continous. It brings about many difficulties in theory and application.
为了得到关于弱集值渐近鞅的收敛性质，首先证明了支撑函数列的极限亦为一支撑函数。
In order to get the convergence properties of the weak set-valued Amart, we firstly proved the theorem that the limit of support functions is a support function.
应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。
By using the limits of functions and the exchange limit theorem, we considered the relationship between the double limit of function with two variables and its repeated limits.
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