Tchebycheff systems and extremal problems for generalized moments: a brief survey

Abstract

A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given. The results, as well as all the necessary definitions, are stated in most common terms. This work is motivated by specific applications in probability and statistics. A few related questions are also briefly discussed, including the one on the existence of a Tchebycheff system on a given topological space.