On page 4 of arXiv:1701.02434v2 ("A Conceptual Introduction to Hamiltonian Monte Carlo"), we have the following text and expectation:
We begin by assuming that the target sample space, $Q$, can be parameterized by the real numbers such that every point $q\in Q$ can be specified with $D$ real numbers. Given a parameter space, $\mathcal{Q}$, we can then specify the target distribution as a smooth probability density function, $\pi(q)$, while expectations reduce to integrals over parameter space,
$$\mathbb{E}_\pi[f] = \int_\mathcal{Q} \text{d}q\pi(q)f(q)$$
The way this integral is written does not make sense to me. I would have expected it to be written as,
$$\mathbb{E}_\pi[f] = \int_\mathcal{Q} \pi(q)f(q) \text{d}q$$
i.e., we are integrating over the target distribution $\pi$ and the function $f$ with respect to $q$, in line with how we write e.g. mean for some random (continuous) variable $X$ and density $p$:
$$\mathbb{E}[X] = \int xp(x)\text{d}x$$
Are these somehow equivalent? Am I misunderstanding either the integral or what this expectation represents?
Steven Stadnicki answered the question in a comment: This is a notation I had never seen, i.e. not keeping the differential at the end of the integral.
Creating this answer so that I can mark the question as solved.