函数列的黎曼积分极限定理的应用

The Limit Problem of Functional Sequence's Riemann-integral

利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在.

By using the limit theorem of functional sequence, we research problems of the integral and limit exchangeable order about the functional sequence＇s integral. We give the limit theorem for the integral functional sequence with uniform convergence. And for the functional sequence with uniform sector and local uniform convergence, we also give the integral dominated convergence theorem. Through the settlement and application of examples, the theory shows its necessity and power.