The theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.

(generalised) regular variation, characteristic function, domain of attraction
Tinbergen Institute Discussion Paper Series
Tinbergen Institute

Geluk, J.L, & de Haan, L.F.M. (1997). Stable Probability Distributions and their Domains of Attraction (No. TI 97-089/4). Tinbergen Institute Discussion Paper Series. Retrieved from