  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.
