Theorem
properties of
lim inf
\liminf
and
lim sup
\limsup
lim inf
A
n
⊂
lim sup
A
n
\liminf A_n \subset \limsup A_n
(
lim inf
A
n
)
∁
=
lim sup
A
n
∁
\left( \liminf A_n \right) ^{\complement} = \limsup A_n^{\complement}