Context: page 18, equation (5.4)
I'm confused by the following notation: $$\int D^{(k)}K_n(x-y)(\Pi_x\tau)(\mathrm{d}y).$$ We have that $K=\sum_{n\geq 0} K_n$, where each $K_n$ is a smooth function $\mathbb{R}^d\to\mathbb{R}$.
$\Pi_x \tau:\mathcal{S}(\mathbb{R}^d)\to\mathbb{R}$ is a tempered distribution (i.e. some generalised function).
I'm confused by the notation. What does it mean to take an integral, with $\mathrm{d}y$ in brackets? If it said something like $$\int D^{(k)}K_n(x-y)(\Pi_x\tau)(y)\mathrm{d}y$$ then that would have made more sense to me, but I don't know how to interpret the above expression.