Definition:Limit Inferior of Extended Real Sequence

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Definition

Let $\sequence {x_n}$ be an extended real sequence.

The limit inferior of $\sequence {x_n}$ is defined as:

$\ds \liminf x_n : = \map {\sup_{k \mathop \ge 1} } {\inf_{n \mathop \ge k} x_n}$


Also see


Sources