A History of the Central Limit Theorem : from Classical to Modern Probability Theory

This book provides a comprehensive history of one of the most important theorems of probability theory and mathematical statistics from about 1810 to ca. 1950. Taking problems surrounding the central limit theorem as characteristic examples, the development of probability theory from its classical form to its modern, and even postmodern, shape is illuminated. The main topics of the book include: Laplace's normal approximations and its applications to natural sciences; Poisson's modifications; Dirichlet's proof; the central limit theorem in the Cauchy-Bienaymé controversy; the development of the hypothesis of elementary errors; the theory of moments and the central limit theorem in Chebyshev's and Markov's work; first steps into modern probability by Lyapunov; contributions by Pólya, von Mises, Lindeberg, Lévy, Bernshtein, and Cramér during the 1920s; Lévy's and Feller's necessary conditions; generalizations toward dependent random variables, nonnormal limit laws, functional limit theorems, and sums of random elements in metric spaces