Hausdorff outer measure is finite if $\sum_{j = 1}^m |f(x_i)-f(x_{i-1})|^s \le c$


Let $ f:[0,1] \to \mathbb{R}, G = graph(f)$ .

If $ \sum_{j = 1}^m |f(x_i)-f(x_{i-1})|^s \le c$ for all partitions $ 0 = x_0< \ldots < x_m = 1 $ then $ H^s(G) < \infty$

What technique can I use to prove this result?

Can it be reduced to the thorem stating that a rectifiable curve $ \Gamma$ has $ H^1(\Gamma) < \infty$ ?