Bernstein Polynomials

A₁ absolutely continuous analytic analytic function approximation arbitrary assume autonomous sets B₂ B₂(x Banach space Bernstein polynomials Bn(x boundary bounded variation C₁ C₂ circle coefficients condition contains continuous function continuous linear functional contour convex corresponding counting function deduce defined denote equation equimeasurable exists fg dx finite following theorem formula g₁ Hausdorff Hence Hölder inequality implies inequality integrable function interval Kantorovitch Kn(x L₂ lemma linear continuous functional loop Lorentz Math matrix measurable functions measurable functions f(x method of summation modulus of continuity moment problem norm obtain Pnv(x points of intersection properties R₁ R₂ rearrangements region satisfies segment sequence Sn(x star-shaped Stieltjes integral subset summability functions Suppose tangent theorem of Weierstrass total variation values zero