Definition:Limit Superior of Sequence of Sets/Notation
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Definition
Let $\set {E_n : n \in \N}$ be a sequence of sets.
The limit superior of $E_n$ can also be seen denoted as:
- $\ds \underset {n \mathop \to \infty} {\overline \lim} E_n$
but this notation is not used on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Some sources merely present this as:
- $\ds \overline \lim E_n$
The abbreviated notation $E^*$ can also be seen.
Sources
- 1951: J.C. Burkill: The Lebesgue Integral ... (previous) ... (next): Chapter $\text {I}$: Sets of Points: $1 \cdot 1$. The algebra of sets
- 1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras