The Hausdorff Moment Problem is a mathematical question that seeks to determine whether a sequence of numbers can be represented as moments of a probability measure on the real line. Moments are specific values derived from a function, often related to its shape and behavior. The problem is named after the mathematician Felix Hausdorff, who contributed significantly to the field of set theory and topology. In essence, the problem asks if a given sequence corresponds to the moments of some non-negative function. If such a function exists, it provides insights into the underlying distribution of the data represented by the moments. The solution involves various mathematical techniques, including functional analysis and measure theory.