Definition:Limit Superior of Sequence of Sets

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

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

Also see

 * Limit Inferior of Sequence of Sets


 * Characterization of Limit Superior of Sets, in which it is proved:
 * $\displaystyle \limsup_{n \to \infty} \ E_n = \left\{{x : x \in E_i \text{ for infinitely many i}}\right\}$