Jessen–Wintner theorem

In mathematics, the Jessen–Wintner theorem, introduced by Jessen and Wintner (1935), asserts that a random variable of Jessen–Wintner type, meaning the sum of an almost surely convergent series of independent discrete random variables, is of pure type.

References

• Jessen, Borge; Wintner, Aurel (1935), "Distribution Functions and the Riemann Zeta Function", Transactions of the American Mathematical Society, 38 (1), Providence, R.I.: American Mathematical Society: 48–88, doi:10.2307/1989728, ISSN 0002-9947, JSTOR 1989728
• Sato, Ken-Iti (1999), Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, ISBN 0521553024