EDB — 166

[166]Let be given \(f : [a, b] →ℝ\) and a decomposition of \([a, b]\) into intervals \(I_ 1 = [a, t_ 1 ], I_ 2 = [t_ 1 , t_ 2 ], \ldots , I_ n = [t_{n-1} , b]\) such that the restriction of \(f\) on each \(I_ k\) is Lipschitz of constant \(C\). Show that \(f\) is Lipschitz of constant \(C\).

Similarly for Hölder functions.