On the Limiting Distribution of the Maximum Term in a Random Series

Let us consider a sequence $$ {x_1},{x_2},...,{x_n},... $$ (1) of mutually independent random variables with a common distribution law F(x). We construct another sequence of variables ξ 1 , ξ 2 ,..., ξ n ,..., putting ξ n =max $$ {x_1},{x_2},...,{x_n},... $$ (2) .