Definition:Limit Inferior of Extended Real Sequence
Jump to navigation
Jump to search
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
- Definition:Limit Superior of Extended Real Sequence
- Existence of Limit Inferior of Extended Real Sequence
Sources
- 1984: Gerald B. Folland: Real Analysis: Modern Techniques and their Applications : $\S P.5$