The Central Limit Theorem Around 1935
A long standing problem of probability theory has been to find necessary and sufficient conditions for the approximation of laws of sums of random variables by Gaussian distributions. A chapter in that search was closed by the 1935 work of Feller and Levy and by a beautiful result of Cramer published in early 1936. We review the respective contributions of Feller and Levy mentioning as necessary contributions of Laplace, Poisson, Lindeberg, Bernstein, Kolmogorov, and others, with an effort to place them in the context of the authors' times and in a modern content.
Permanent link to this document: http://projecteuclid.org/euclid.ss/1177013818
Digital Object Identifier: doi:10.1214/ss/1177013818
Mathematical Reviews number (MathSciNet): MR833276