Theorem
intuitive interpretation of
lim inf
\liminf
and
lim sup
\limsup
lim sup
A
n
=
{
ω
:
∑
n
=
1
∞
1
A
n
(
ω
)
=
∞
}
\limsup A_n = \left\{ \omega : \sum_{n=1}^{\infty} 1_{A_n}(\omega) = \infty \right\}
lim inf
A
n
=
{
ω
:
∑
n
=
1
∞
1
A
n
∁
(
ω
)
<
∞
}
\liminf A_n = \left\{ \omega : \sum_{n=1}^{\infty} 1_{A_{n}^\complement}(\omega) \lt \infty \right\}