## 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 $$H^1(\Gamma) < \infty$$?