Geodesic
A Note on Normal Attraction to a Stable Law
Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 451-452

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Let X 1, X 2, ..., be a sequence of independent and identically distributed random variables, with the common distribution function F(x). The sequence is said to be normally attracted to a stable law V with characteristic exponent α, if for some an (converges in distribution to V). Necessary and sufficient conditions for normal attraction are known (cf [1, p. 181]). 
Menon, M. V.; Seshadri, V. A Note on Normal Attraction to a Stable Law. Canadian mathematical bulletin, Tome 14 (1971) no. 3, pp. 451-452. doi: 10.4153/CMB-1971-081-5
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[1] 1. Gnedenko, B.V. and Kolmogorov, A. N., Limit distributions for sums of independent random variables, Addison-Wesley, Reading, Mass., 1954. Google Scholar

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