Let $s \in [0,1[$. Suppose that the function $h \mapsto \frac{\omega_{f}(h)}{h^{s}}$ is bounded on $]0,1]$. For all $x_{0} \in [0,1]$, show that $f \in \Gamma^{s}(x_{0})$.
Let $s \in [0,1[$. Suppose that the function $h \mapsto \frac{\omega_{f}(h)}{h^{s}}$ is bounded on $]0,1]$. For all $x_{0} \in [0,1]$, show that $f \in \Gamma^{s}(x_{0})$.