This paper studies the L(p) approximation capabilities of sum-of-product (SOPNN) and sigma-pi-sigma (SPSNN) neural networks. It is proved that the set of functions that are generated by the SOPNN with its activation function in $L_{loc};p(\mathcal{R})$ is dense in $L;p(\mathcal{K})$ for any compact set $\mathcal{K}\subset \mathcal{R};N$, if and only if the… (More)