# Definitions for limsup and also liminf

I was questioning what are the basic rooms that the principles limsup and also liminf can relate to? Is full latticework among them? Additionally How around statistics room?

What are limsup and also liminf defined relative to? A part? A sequence/net/filter base?

The amount of sort of interpretations for limsup and also liminf in these numerous instances? Are they equal? Otherwise, what are the problems for them to be equal?

0
2019-05-18 22:36:18
Source Share
The idea of a $\limsup$ of a filteringed system routed set makes good sense. Particularly, allow $A$ be a filtered routed set and also $x_\alpha, \alpha \in A$ be an $A$ - indexed family members in $\mathbb{R}$. After that one can specify the $\limsup$ as the infimum of $\sup_{\beta > \alpha} x_{\beta}$ over all $\alpha$. This makes good sense for the $\liminf$ too.