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 by[GRAPHICS]where a(j), theta(j), w(ji) is an element of R. In this paper we study the approximation of arbitrary functions f: R-d --> R by a neural net in an L-p(mu) norm for some finite measure mu on R-d. We prove that under natural moment conditions, a neural net with non-polynomial function can approximate any given function. (C) 1998 Elsevier Science Ltd. All rights reserved.