Bernstein's theorem (polynomials)

Bernstein's theorem in the context of polynomials refers to results concerning the approximation of continuous functions by polynomials, particularly in relation to the uniform convergence of polynomial sequences. One of the key results of Bernstein's theorem states that if \( f \) is a continuous function defined on a closed interval \([a, b]\), then \( f \) can be approximated arbitrarily closely by polynomials in the uniform norm.