Category:Definitions/Limits Superior of Set Sequences

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

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

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

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

$:=$

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

$\ds $

$=$

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

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

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