The limit distribution of the extreme terms of the variational series under the large deviation type conditions for the sample mean .

Let $x_1,\dots x_n$ be independent observations of a random variable $\xi$, $\underline x=\min\limits_{1\le i\le n}x_i$, $\overline x=\max\limits_ {1\le i\le n}x_i$. Some theorems are proved concerning the distribution of $\underline x$ and $\overline x$ under the condition that the sum $x_1+\dots+x_n$ is large.