Definition:Limit Superior/Definition 2

Definition

Let $\sequence {x_n}$ be a bounded sequence in $\R$.

The limit superior of $\sequence {x_n}$ is defined and denoted as:

$\ds \map {\limsup_{n \mathop \to \infty} } {x_n} = \inf \set {\sup_{m \mathop \ge n} x_m: n \in \N}$

Also see

• Equivalence of Definitions of Limit Superior

Linguistic Note

The plural of limit superior is limits superior.

This is because limit is the noun and superior is the adjective qualifying that noun.

Sources

• 2005: René L. Schilling: Measures, Integrals and Martingales ... (previous) ... (next): $\S 8$