Weierstrass逼近定理及其应用

WEIERSTRASS APPROXIMATION THEOREM AND IT'S APPLICATION

4 Weierstrass定理的推广—Stone定理这一节所介绍的Stone定理是Weierstrass定理的推广。由此可以得到其他的逼近定理。我们先从一系列的引理开始。引理5 设x1,x2∈[a,b],x1≠x2,（?）[a,b]上（?）函数（x）:且Φ（x）在[a,b]上能被多项式一致逼近。证任取一个多项式P（x）,只要作P（x1）≠P（x2）,这是可以办到的,例如职P（x）=x。

In this paper we give out weierstrass approximationn theorem and it's extended strict proof, and expound in a contact with relevant theorem.