Determinacy of a distribution with finitely many mass points by finitely many moments

Abstract

We consider the determinacy problem for a distribution function F(x), x∈R, by mixed data consisting of partial information given on F and knowing its finitely many moments. Necessary and sufficient conditions for solvability of the problem are derived. Essential is the established one-to-one correspondence between the Hamburger moment problem with finitely many moments and a discrete positive Borel measure concentrated at finitely many points on the real axis.