The Stieltjes Moment Problem is a mathematical question that seeks to determine whether a sequence of moments can correspond to a probability measure. Moments are specific numerical values that summarize certain characteristics of a distribution, such as its mean and variance. The problem is named after the mathematician Thomas Joannes Stieltjes, who studied these relationships in the late 19th century. In essence, the Stieltjes Moment Problem asks if a given sequence of numbers can be derived from a function that describes a probability distribution. This involves finding a function that satisfies certain conditions, such as being non-negative and integrating to one. Solutions to this problem have applications in various fields, including statistics and physics.