  We discuss the expressive power of neural networks which use the non-smooth
ReLU activation function $\varrho(x) = \max\{0,x\}$ by analyzing the
approximation theoretic properties of such networks. The existing results
mainly fall into two categories: approximation using ReLU networks with a fixed
depth, or using ReLU networks whose depth increases with the approximation
accuracy. After reviewing these findings, we show that the results concerning
networks with fixed depth--- which up to now only consider approximation in
$L^p(\lambda)$ for the Lebesgue measure $\lambda$--- can be generalized to
approximation in $L^p(\mu)$, for any finite Borel measure $\mu$. In particular,
the generalized results apply in the usual setting of statistical learning
theory, where one is interested in approximation in $L^2(\mathbb{P})$, with the
probability measure $\mathbb{P}$ describing the distribution of the data.
