关于Weierstrass逼近定理的推广  

On the Generalization of Weierstrass Approximation Theorem

作　　者：牛英春[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2010年第6期614-616,共3页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：内蒙古民族大学硕(博)士科研启动基金

摘　　要：Welerstrass逼近定理是函数逼近论中的重要理论之一,定理阐述了闭区间上的连续函数可以用多项式去逼近,当函数为几乎处处连续时也有类似的逼近性质.将定理再次推广,证明了定义在闭区间上的基本连续函数基本保持了类似的逼近性质,并给出了Weistrass逼近定理的推广应用.Weierstrass Approximation Theorem is one of important theories in Appreximation Theorem,The theorg elaborates that continuous functions can be approached by polynomials,Analogous approximation characters can be obtained by almost everyuhere continuous functions.This paper generalizes weierstrass Approximation Theorem once again,obtains a result that basic continuous functions basically hold the approximation character in closed interval,In addition,deals with application on the result.

关 键 词：WEIERSTRASS逼近定理 基本连续 测度 

分 类 号：O174.41[理学—数学]