Category:Limits Inferior of Set Sequences

This category contains results about Limits Inferior of Set Sequences.
Definitions specific to this category can be found in Definitions/Limits Inferior of Set Sequences.

Let $\set {E_n : n \in \N}$ be a sequence of sets.

Then the limit inferior of the sequence, denoted $\displaystyle \liminf_{n \mathop \to \infty} \ E_n$, is defined as:

 $\displaystyle \liminf_{n \mathop \to \infty} \ E_n$ $:=$ $\displaystyle \bigcup_{n \mathop = 0}^\infty \ \bigcap_{i \mathop = n}^\infty E_n$ $\displaystyle$ $=$ $\displaystyle \paren {E_0 \cap E_1 \cap E_2 \cap \ldots} \cup \paren {E_1 \cap E_2 \cap E_3 \cap \ldots} \cup \cdots$

Pages in category "Limits Inferior of Set Sequences"

The following 5 pages are in this category, out of 5 total.