Definition:Limit Inferior of Sequence of Sets

Definition
Suppose $\left\{{E_n : n \in \N}\right\}$ is a sequence of sets.

Then the limit inferior of the sequence, denoted $\displaystyle \liminf_{n \to \infty} \ E_n$, is defined as:

Also see

 * Limit Superior of a Sequence of Sets


 * Characterization of Limit Inferior of Sets, in which it is proved:
 * $\displaystyle \liminf_{n \to \infty} \ E_n = \left\{{x : x \in E_i \text{ for all but finitely many} \ i}\right\}$