Stieltjes Approximations

Stieltjes approximations are a mathematical method used to estimate complex functions or distributions by representing them as sums of simpler, weighted components called measures. Essentially, they break down complicated data or functions into a series of basic building blocks, making calculations and analysis easier. This approach is often employed in areas like probability, numerical analysis, and approximation theory to efficiently approximate integrals or functions, especially when direct computation is difficult. By doing so, Stieltjes approximations help us understand, analyze, and compute properties of functions with greater accuracy and efficiency.