Geodesic
On an estimate of the remainder in Lindeberg's theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 1, pp. 141-143

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Let $X_1,X_2,\dots$ be a sequence of independent random variables which have the distribution functions $F_1(x),F_2(x),\dots$, the mean values $m_1,m_2,\dots$, the finite variances $\sigma_1^2,\sigma_2^2\dots$ and infinite absolute moments of order $2+\delta$ for any $\delta>0$. The examples of sequences are given for which the estimate $$ \sup_x|F_n(x)-\Phi(x)|\le C\Psi_n(\varepsilon s_n) $$ does not hold true. Here $C$ is a constant, $\varepsilon$ is any fixed positive number and $F_n(x)$, $\Phi(x)$, $\Psi_n(\varepsilon s_n)$ are defined on p. 141. 
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     author = {I. A. Ibragimov and L. V. Osipov},
     title = {On an estimate of the remainder in {Lindeberg's} theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1966},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_1_a7/}
}
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I. A. Ibragimov; L. V. Osipov. On an estimate of the remainder in Lindeberg's theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 1, pp. 141-143. http://geodesic.mathdoc.fr/item/TVP_1966_11_1_a7/