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Let
 be a sequence of sets. The limit superior of sets is defined by
It is easy to see that
 if and only if  for infinitely many values of  . Because of this, in probability theory the notation
![$ [A_n \operatorname{i.o.}]$](http://images.planetmath.org:8080/cache/objects/3689/l2h/img6.png "$ [A_n \operatorname{i.o.}]$") is often used to refer to
 , where i.o. stands for infinitely often.
The limit inferior of sets is defined by
and it can be shown that
 if and only if  belongs to  for all but finitely many values of  .
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