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At present this article is little more than a disambiguation page. What names would you give to the two theorems? I just found an article (in French) where the first theorem (on the sum of two independent random variables) is called "[le] théorème de Lévy-Cramer" (H. ROUANET, B. LECLERC Le rôle de la distribution normale en statistique Mathématiques et sciences humaines, vol. 32 (1970), p. 57-74. http://www.numdam.org/item?id=MSH_1970__32__57_0 ) Perhaps we can call this theorem the Lévy–Cramér theorem to disambiguate from Cramér's other theorem (on large deviations), which also seems to go by the name "Cramér's theorem"? Deepmath (talk) 08:00, 25 December 2008 (UTC)[reply]
Yes, I agree. Another ref: Section 8.8 "The Lévy-Cramér theorem" in book: David Pollard, "A user's guide to measure theoretic probability", Cambridge Univ. Press 2002. Boris Tsirelson (talk) 08:57, 25 December 2008 (UTC)[reply]
Unfortunately, there seems to be yet another theorem that goes by the name of Lévy–Cramér: it has to do with the convergence of the characteristic functions of a sequence of probability distributions. I'm getting lost again... But there is a nice proof in the book you mentioned. Deepmath (talk) 09:11, 25 December 2008 (UTC)[reply]
