Geodesic
The strong law of large numbers and the normality of Kesten's procedure
Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 637-643

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The normality of Kesten's procedure and other consequences are deduced from a generalization of the strong law of large numbers. 
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S. V. Žulenev; V. S. Medovyǐ. The strong law of large numbers and the normality of Kesten's procedure. Teoriâ veroâtnostej i ee primeneniâ, Tome 23 (1978) no. 3, pp. 637-643. http://geodesic.mathdoc.fr/item/TVP_1978_23_3_a14/