For example, the inequality
$$\left|\int_\gamma f(z)\,dz\right|\leq \int_\gamma |f(z)|\,d|z|. $$
What does '$d|z|$' mean in this context?
Edit: I suppose it's better to mention the whole problem itself. My notes say that
$$\int_{c+iT}^{\infty+iT} y^{\Re(s)}d|s| = \int_{c}^{\infty} y^{\sigma}d\sigma $$
and I don't understand why this is true.