Let $G$ be a locally compact group with left Haar measure $\mu$. If $f: G \rightarrow \mathbb{C}$ is an integrable function, and $E \subseteq G$, the notation
$$\int_E f(g)dg$$
is commonly used instead of $$\int\limits_E f d\mu$$
It is also common to write things like $\int\limits_E f(g)d(gh^{-1})$ for a fixed $h \in H$. This seems to be somewhat like u-substitution, although there should be some formal measure theory behind it. Would anyone be willing to explain or give a reference which explains the measure-theoretic principles behind the use of such notation?