  We study the approximation of measurable functions on the hypercube by
functions arising from affine neural networks. Our main achievement is an
approximation of any measurable function $f \colon W_n \to [-1,1]$ up to a
prescribed precision $\varepsilon>0$ by a bounded number of neurons, depending
only on $\varepsilon$ and not on the function $f$ or $n \in \mathbb N$.
