EDB — 15W

Exercises

1. [15W] Let \(I⊆ℝ\) be an interval, and let \(f:I→ℝ\) be uniformly continuous. Let \(𝜔\) be the continuity modulus, defined by the eqz. [(13.16)]↺↻, as in the exercise [156]↺↻. Show that \(𝜔\) is subadditive i.e.

   \[ 𝜔(t)+𝜔(s)≥ 𝜔(t+s)\quad . \]

   Knowing that \(\lim _{t→ 0+}𝜔(t)=0\) we conclude that \(𝜔\) is continuous.

   Solution 1

   [15X]↺↻

   [ [15Y]↺↻]