Definition:Limit Superior of Extended Real Sequence

Definition

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

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

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

Also see

• Definition:Limit Inferior of Extended Real Sequence
• Existence of Limit Superior of Extended Real Sequence

Sources

• 1984: Gerald B. Folland: Real Analysis: Modern Techniques and their Applications : $\S P.5$