关于weierstrass逼近定理的几点注记

Weierstrass逼近定理是函数逼近论中的重要定理之一,定理阐述了闭区间上的连续函数可以用一多项式去逼近.将该定理进行推广:即使一个函数是几乎处处连续的,也不一定具有与连续函数相类似的逼近性质,但是一个处处不连续的函数却有可能具有这样的性质.证明了定义在闭区间上且与连续函数几乎处处相等的函数具有类似的逼近性质,并给出了weierstrass逼近定理的一个推广应用.

Some Notes on Weierstrass Approximation Theorem

The weierstrass approximation theorem is one of the important theorems in functional approximation theories.This theorem tells us that the continuous function defined on closed interval can be approximated by a polynomial.The weierstrass approximation theorem is generalized: For a function is almost everywhere continuous,it does not always have the similar approximation property as the continuous function,while a discontinuous function in everywhere can has the similar property.The proof of the approximate features of the function which is almost everywhere equal to a continuous function in the closed interval is discussed.And a generalized application of the weierstrass approximation theorem is given finally.