L_p范数下随机连续函数空间中的Weierstrass定理  

Weierstrass's theorem in L_p spaces of random continuous function

作　　者：陈英伟[1] 王志军[1] CHEN Yingwei;WANG Zhijun(College of Mathematics and Statistics,Hebei University of Economics and Business,Shijiazhuang 050061,China)

机构地区：[1]河北经贸大学数统学院,河北石家庄050061

出　　处：《河北大学学报（自然科学版）》2018年第1期7-11,共5页Journal of Hebei University(Natural Science Edition)

基　　金：河北省自然科学基金资助项目(A2015207007);河北省科技计划项目(17210310D)

摘　　要：通过概率方法对随机连续函数的多项式逼近性质进行了研究.借助随机Bernstein算子给出了Lp范数下随机系数多项式逼近的定性估计,进而推广了Weierstrass定理.The purpose of this article is to investigate polynomial approximation properties of random continuous function by the probability method.We obtained the qualitative estimation by random Bernstein’s operator with L p norm and extended Weierstrass's theorem to random continuous function spaces further.

关 键 词：随机连续函数 WEIERSTRASS定理 随机Bernstein算子 随机系数多项式 

分 类 号：O174.41[理学—数学]