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:

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