Category:Limits Inferior of Set Sequences
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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 $\sequence {E_n : n \in \N}$ 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 "Limits Inferior of Set Sequences"
The following 5 pages are in this category, out of 5 total.