函数列一致收敛的奥斯古德定理  

The Osgood Theorem of Uniformly Convergent Functions

作　　者：邢家省[1,2] 杨义川[1,2] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191 [2]数学信息与行为教育部重点实验室,北京100191

出　　处：《四川理工学院学报（自然科学版）》2017年第6期83-87,93,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11271040);北京航空航天大学校级重大教改项目(201403)

摘　　要：研究函数列的一致收敛性的理论方法问题,在有限闭区间上,给出了判断函数列一致收敛的奥斯古德定理和狄尼定理的两种形式,对奥斯古德定理给出了两种证明方法,给出了奥斯古德定理的几个推论,沟通了相关知识的联系,并通过实例说明奥斯古德定理的应用及其理论价值。在开区间或无限区间上,给出了函数列一致收敛的判别定理,并应用于研究含参变量广义积分的一致收敛性,从理论上沟通了函数列一致收敛与参变量广义积分的一致收敛的内在联系,构成一套理论方法体系。Considering the theoretical method of uniformly convergent functions,Osgood theorem and the Dini theorem on the finite interval are given to judge the uniform convergence of Function column. Then two proof methods of Osgood theorem and its inference are given. And through the examples,the theoretical value of Osgood theorem is illustrated. Discriminant theorem of uniform convergence of function in open or infinite interval have been given and applied in studying the uniform convergence of generalized integrals with parametric variables which theoretically communicating the intrinsic relations between the uniform convergence of the function and the uniform convergence of the parameter generalized integral,and forming a set of theoretical method system.

关 键 词：函数列的一致收敛性 等度一致连续 奥斯古德定理 狄尼定理 

分 类 号：O177.2[理学—数学]