EDB — 064

Exercises

1. [064] Prerequisites:[018]↺↻. Show that

   \begin{eqnarray} \label{eq:limsup_ insiemi_ freq} \limsup _{n→∞} A_ n & =& \{ x∈ X : x∈ A_ n \text{ frequently in~ }n\} ~ ~ ,\\ \label{eq:liminf_ insiemi_ defn} \liminf _{n→∞} A_ n & =& \{ x∈ X : x∈ A_ n \text{ eventually in~ }n\} ~ ~ . \end{eqnarray}

   (”Frequently” and ”eventually” are discussed in Sec. [26G]↺↻).