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The Generalized Central Limit Theorem

The Generalized Central Limit Theorem (GCLT) was an effort of multiple mathematicians (Bernstein, Lindeberg, Lévy, Feller, Kolmogorov, and others) over the period from 1920 to 1937. The first published complete proof of the GCLT was in 1937 by Paul Lévy in French. An English language version of the complete proof of the GCLT is available in the translation of Gnedenko and Kolmogorov 's 1954 book.

The statement of the GCLT is as follows:

In other words, if sums of independent, identically distributed random variables converge in distribution to some Z, then Z must be a stable distribution.