= Bernstein's theorem (approximation theory)
{wiki=Bernstein's_theorem_(approximation_theory)}
Bernstein's theorem in the context of approximation theory, particularly in the field of polynomial approximation, refers to the result that relates to the uniform approximation of continuous functions on a closed interval using polynomial functions. The theorem states that if \\( f \\) is a continuous function defined on the interval \\(\[a, b\]\\), then \\( f \\) can be uniformly approximated as closely as desired by a sequence of polynomials.
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