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Definition 285

[1Z2](Solved on 2022-11-29) Given \(A_ 1,A_ 2\ldots \) sets , for \(nβˆˆβ„•\), we define

\begin{eqnarray} \label{eq:limsup_ insiemi} \limsup _{nβ†’βˆž} A_ n {\stackrel{.}{=}}β‹‚_{n=1}^∞ ⋃_{k=n}^∞ A_ k\\ {} \label{eq:liminf_ insiemi} \liminf _{nβ†’βˆž} A_ n {\stackrel{.}{=}}⋃_{n=1}^∞ β‹‚_{k=n}^∞ A_ k\\ {} \end{eqnarray}

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