Weierstrass approximation theorem

If f is a continuousPlanetmathPlanetmath real-valued function on a interval [a,b] then for all ε>0 there exists a polynomialPlanetmathPlanetmath P which satisfies |f(x)-P(x)|<εx[a,b] This theorem also holds for compact subsets of n. The Stone-Weierstrass theorem is a generalizationPlanetmathPlanetmath to even more general situations.

Title Weierstrass approximation theoremMathworldPlanetmath
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