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For questions concerning limit superior and limit inferior of sequences (of real numbers and various generalizations) and also for $\limsup$ and $\liminf$ of sequences of sets.
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When are events in tail $\sigma$-algebra the limsup of some sequence of events?
Consider a sequence of $\sigma$-algebras $\mathcal{F}_1,\mathcal{F}_2,\dots$. Is it true that for any event $B$ in the tail $\sigma$-algebra $\mathcal{F_{\text{Tail}}}$, it can be expressed as the $\l …