Geodesic
On the necessity of the Lyapunov condition for normal convergence
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 173-175

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This paper provides necessary and sufficient conditions for the weak convergence of the distributions of sums of independent random variables to the normal distribution. The conditions are given as a combination of a part of the assumption of the classic criterion for the normal convergence and the Lyapunov condition for truncated random variables.
Mots-clés : normal convergence
Keywords: Lindeberg–Feller theorem, weak convergence, Lyapunov condition. 
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     author = {V. M. Kruglov},
     title = {On the necessity of the {Lyapunov} condition for normal convergence},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {173--175},
     publisher = {mathdoc},
     volume = {52},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a10/}
}
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V. M. Kruglov. On the necessity of the Lyapunov condition for normal convergence. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 1, pp. 173-175. http://geodesic.mathdoc.fr/item/TVP_2007_52_1_a10/