Bernstein's Theorem on Monotone Functions

Bernstein's theorem on monotone functions, named after Sergei Bernstein, states that every real-valued function on the half-line [0, infinity) that is completely monotone can be written as a mixture of exponential functions, equivalently as the Laplace transform of a positive Borel measure on that half-line. In the special case where the mixture is a weighted average, it corresponds to an expected value, and the result is also known as the Bernstein-Widder theorem or the Hausdorff-Bernstein-Widder theorem. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/