Universal approximation in p-mean by neural networks.

A feedforward neural net with d input neurons and with a single hidden layer of n neurons is given byg(x(1), em leader,x(d))= summation operator j=1na(j)sigma,where a(j), theta(j), w(ji) in R. In this paper we study the approximation of arbitrary functions F:R(d)-->R by a neural net in an L(p)(&mgr;) norm for some finite measure &mgr; on R(d). We prove that under natural moment conditions, a neural net with non-polynomial function can approximate any given function.