Sigma-Ring contains Limit Superior of Sequence of Sets

Theorem

Let $\RR$ be a $\sigma$-ring.

Let $\sequence {A_n}_{n \mathop \in \N} \in \RR$ be a sequence of sets in $\RR$.

Then:

$\ds \limsup_{n \mathop \to \infty} A_n \in \RR$

Proof

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Sources

• 1970: Avner Friedman: Foundations of Modern Analysis ... (previous) ... (next): $\S 1.1$: Rings and Algebras: Problem $1.1.3$