5. Approximation by finite-width networks
This chapter is Section 6 of the manuscript together with Appendix D. Exact representation uses a continuous parameter integral; finite width is obtained by sampling the coefficient measure, with no projection of the input space or of the direction parameter. The sampling bounds come first, then the coefficients produced by the spectral representation are shown to satisfy their hypotheses, and both are combined with the density of targets with a spectral density into the approximation theorem Theorem 5.3.1.