Weierstrass approximation theorem

If $f$ is a continuous real-valued function on a interval $[a,b]$ then for all $\varepsilon>0$ there exists a polynomial $P$ which satisfies $|f(x)-P(x)|<\varepsilon\quad\forall x\in[a,b]$ This theorem also holds for compact subsets of $\mathbb{R}^{n}.$ The Stone-Weierstrass theorem is a generalization to even more general situations.

Title	Weierstrass approximation theorem
Canonical name	WeierstrassApproximationTheorem
Date of creation	2013-03-22 14:34:52
Last modified on	2013-03-22 14:34:52
Owner	Tobi (6409)
Last modified by	Tobi (6409)
Numerical id	7
Author	Tobi (6409)
Entry type	Theorem
Classification	msc 41A10