Geodesic
Another proof of a~Sakhanenko theorem
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 591-596

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We give an analytic proof of Sakhanenko's theorem on the strong law of large numbers. Our arguments are based on the method of characteristic functions: under the Lindeberg-type condition, the expectation of the absolute value of the sum of independent random variables (r.v.'s) tends to zero. In our proof, we represent the expectation of the absolute value of an r.v. in terms of the corresponding characteristic function.
Keywords: random variable, characteristic function, strong law of large numbers. 
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     author = {Sh. K. Formanov},
     title = {Another proof of {a~Sakhanenko} theorem},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {591--596},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a9/}
}
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Sh. K. Formanov. Another proof of a~Sakhanenko theorem. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 3, pp. 591-596. http://geodesic.mathdoc.fr/item/TVP_2022_67_3_a9/