The Chebyshev approximation problem is usually described as to find the polynomial (or the element of an Haar subspace) which uniformly best approximates a given continuous function. Most of the theoretical results forming the basis of this theory have not been explored by members of the St Petersburg Mathematical School, founded by P. L. Chebyshev himself. The present article briefly wants to explain why. We show that the interests of Chebyshev and his most narrow pupil, A. A. Markov sr.

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... ed on a more algebraic problem, solved only in 1960s by Meyman and required techniques far away from what mathematicians were able to deal with at that time. MSC 2000. 41-03, 01A55, 01A60.