EDB — 13Z

Exercises

1. [13Z]Let \(f_ 1:[0,∞]→ [0,∞]\) monotonic function (weakly increasing) and right continuous. Let then \(f_ 2:[0,∞)→[0,∞]\) be given by

   \[ f_ 2 (s) = \sup \{ t≥ 0 : f_ 1 (t) {\gt} s\} \]

   (with the convention that \(\sup ∅ =0\)) and then again \(f_ 3:[0,∞)→[0,∞]\) defined by

   \[ f_ 3 (s) = \sup \{ t≥ 0 : f_ 2 (t) {\gt} s\} \quad : \]

   then \(f_ 1≡ f_ 3\).

   Solution 1

   [140]↺↻