# 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 WeierstrassApproximationTheorem 2013-03-22 14:34:52 2013-03-22 14:34:52 Tobi (6409) Tobi (6409) 7 Tobi (6409) Theorem msc 41A10