It is shown that for a stationary sequence of random variables
X
1
,
X
2
,
⋯
{X_1},{X_2}, \cdots
one has
\[
lim
inf
n
−
1
∑
i
=
1
n
X
i
>
0
\lim \inf {n^{ - 1}}\sum \limits _{i = 1}^n {{X_i} > 0}
\]
a.e. on the set
{
Σ
1
n
X
i
→
∞
,
n
→
∞
}
\{ \Sigma _1^n{X_i} \to \infty ,n \to \infty \}
.