We have the following well know definition:
If $\gamma: [a,b] \to \mathbb{R}^{n}$ is an injective and continuously differentiable function, then the length of $\gamma$ is defined as the quantity $$\operatorname{Length}(\gamma) ~ \stackrel{\text{def}}{=} ~ \int_{a}^{b} |\gamma'(t)| ~ \mathrm{d}{t}.$$
If I now take a Lipschitz curve $c:[a,b] \to \mathbb{R}^{n}$, then we have by Rademacher theorem $\gamma$ is differentiable almost everywhere with respect to the Lebesgue measure. Do we have in this case too, that $$\operatorname{Length}(c) = \int_{a}^{b} |c'(t)| ~ \mathrm{d}{t}?$$ Many thanks for some help!