Entropy-Convergence in Stieltjes and Hamburger Moment Problem

In the classical Stieltjes and Hamburger's moment problem the sequence of maximum entropy approximants, whose first M moments are equal to given ones, is considered. It is proved that whenever an infinite moment problem is determined then maximum entropy approximants converge in entropy to the function characterized by given moments. Entropy-convergence is proved by using exclusively existence and uniqueness conditions