EDB — 165

Exercises

1. [165]Let \(I⊂ ℝ\) interval. Let \(f : I → ℝ\) such that there exists \(α {\gt} 1\) such that \(∀ x, y, |f (x) − f (y)| ≤ |x − y|^α\) (i.e. \(f\) is Hölder continuous of order \(𝛼{\gt}1\)): Show that f is constant.