Geodesic
The property of extendability of limit distributions for the maximum term of a sequence
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 11-20

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Let $\xi_1,\xi_2,\dots$ be a sequence of identically distributed independent random variables, and let $$ \eta_n=\max(\xi,\xi_2,\dots,\xi_n). $$ The following theorem is proved: If for a certain choice of constants $b_n>0$ and $a_n$ $$ P\biggl\{\frac1{b_n}(\eta_n-a_n)\biggr\}\to\Phi(x),\quad n\to\infty, $$ where $\Phi(x)$ is one of the three possible limiting distributions, and if the convergence is fulfilled in an interval $(c,d)$ for which $\Phi(d)-\Phi(c)>0$, then the convergence holds for all values of $x$. Библиогр. 5. 
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     author = {B. V. Gnedenko and L. Senusi-Bereksi},
     title = {The property of extendability of limit distributions for the maximum term of a sequence},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {11--20},
     publisher = {mathdoc},
     number = {3},
     year = {1983},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/}
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B. V. Gnedenko; L. Senusi-Bereksi. The property of extendability of limit distributions for the maximum term of a sequence. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (1983), pp. 11-20. http://geodesic.mathdoc.fr/item/VMUMM_1983_3_a2/