  In this work, we consider the approximation of a large class of bounded
functions, with minimal regularity assumptions, by ReLU neural networks. We
show that the approximation error can be bounded from above by a quantity
proportional to the uniform norm of the target function and inversely
proportional to the product of network width and depth. We inherit this
approximation error bound from Fourier features residual networks, a type of
neural network that uses complex exponential activation functions. Our proof is
constructive and proceeds by conducting a careful complexity analysis
associated with the approximation of a Fourier features residual network by a
ReLU network.
