Definition:Limit Inferior of Sequence of Sets/Definition 1

Definition
Let $\set {E_n : n \in \N}$ be a sequence of sets.

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

Also see

 * Equivalence of Definitions of Limit Inferior of Sequence of Sets