Category:Definitions/Limits Inferior of Set Sequences

This category contains definitions related to Limits Inferior of Set Sequences.
Related results can be found in Category:Limits Inferior of Set Sequences.

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

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

$\ds \liminf_{n \mathop \to \infty} E_n$

$:=$

$\ds \bigcup_{n \mathop = 0}^\infty \bigcap_{i \mathop = n}^\infty E_n$

$\ds $

$=$

$\ds \paren {E_0 \cap E_1 \cap E_2 \cap \ldots} \cup \paren {E_1 \cap E_2 \cap E_3 \cap \ldots} \cup \cdots$

Pages in category "Definitions/Limits Inferior of Set Sequences"

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