In mathematics, the Stieltjes moment problem, named after Thomas Joannes Stieltjes, seeks necessary and sufficient conditions for a sequence (m0, m1, m2, ...) to be of the form for some measure μ. If such a function μ exists, one asks whether it is unique. The essential difference between this and other well-known moment problems is that this is on a half-line [0, ∞), whereas in the Hausdorff moment problem one considers a bounded interval [0, 1], and in the Hamburger moment problem one considers the whole line (−∞, ∞). Existence Let and Then { mn : n = 1, 2, 3, ... } is a moment sequence of some measure on with infinite support if and only if for all n, both { mn : n = 1, 2, 3, ... } is a moment sequence of some measure on with finite support of size m if and only if for all , both and for all larger Uniqueness There are several sufficient conditions for uniqueness, for example, Carleman's condition, which states that the solution is unique if References Probability problems Mathematical analysis Moment (mathematics) Mathematical problems