Geodesic
On the rate of convergence to the normal law equivalent to the existence of the second moment
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 180-185 
V. A. Egorov. On the rate of convergence to the normal law equivalent to the existence of the second moment. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 180-185. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a16/
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     author = {V. A. Egorov},
     title = {On the rate of convergence to the normal law equivalent to the existence of the second moment},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {180--185},
     year = {1973},
     volume = {18},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a16/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\{X_n\}$ be a sequence of mutually independent identically distributed random variables which belong to the domain of attraction of the normal law. The rate of convergence to the normal law equivalent to the existence of the second moment of $X_n$ is investigated.