Before revision: This article conerns the expressive power of depth in neural nets with ReLU activations . We prove that ReLU nets with width 2d+2 can approximate any continuous scalar function on the d-dimensional cube [0,1]^d arbitrarily well.
After revision: This article conerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width w_{\text{min that ReLU nets with width 2d+2 can approximate any continuous scalar function on the d-dimensional cube [0,1]^d arbitrarily well.