EDB — 063

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Exercises

  1. [063] Recall that

    \[ A^ c=X⧵ A=\{ x∈ X:x∉ A\} \]

    is the complement of \(A\) in \(X\) (as defined in [23S]). Show that

    \[ (\limsup _{n\to \infty } A_ n)^ c=\liminf _{n\to \infty } (A_ n ^ c)~ ~ . \]
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Authors: "Mennucci , Andrea C. G." .
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  • limsup, of sets
  • liminf, of sets
  • set, complement of a ---
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