Geodesic
An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions
Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 3, pp. 311-321 Cet article a éte moissonné depuis la source Math-Net.Ru

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The proof is based on the “information functional” $-(\int_{-\infty}^{+\infty}{p(x)\ln p(x)\,dx}+\frac12\ln\mathbf D(x))$, $p(x)$ being the density of the random variable $X$. Some new dependencies between the Shannon and Fisher information quantities are established and an information theoretic interpretation of the Lindeberg condition is given. 
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     author = {Yu. V. Linnik},
     title = {An {Information-Theoretic} {Proof} of the {Central} {Limit} {Theorem} with {Lindeberg} {Conditions}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {311--321},
     year = {1959},
     volume = {4},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1959_4_3_a3/}
}
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Yu. V. Linnik. An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions. Teoriâ veroâtnostej i ee primeneniâ, Tome 4 (1959) no. 3, pp. 311-321. http://geodesic.mathdoc.fr/item/TVP_1959_4_3_a3/