EDB — 1JQ

Exercises

1. [1JQ]Let \(f:ℝ→ℝ\) and let \(g_ t:ℝ→ℝ\) be the translations of \(f\), defined (for \(t∈ℝ\)) by \(g_ t(x)=f(x-t)\). Show that \(g_ t\) tends pointwise to \(f\) for \(t→ 0\), if and only if \(f\) is continuous; and that \(g_ t\) tends uniformly to \(f\) for \(t→ 0\), if and only if \(f\) is uniformly continuous.

   Solution 1

   [1JR]↺↻