The generalized function γ$_{g}$ is such that there exists a deterministic sequence of regular functions, ( γ$_{g}$ ) n that converges to γ$_{g}$ in S ∗ and such that support of ( γ$_{g}$ ) n is in a compact set Λ$_{gn}$; there exists ζ$_{0}$ > 0 such that ∣ ( γ$_{g}$ ) n ∣ > 2 ζ$_{0}$ and for γ$_{L}$$_{1}$ = F t ( g$_{L}$$_{1}$ ) on Λ$_{g}$ ∣ γ$_{L}$$_{1}$ − ( γ$_{g}$ ) n ∣ > ζ$_{0}$ . Assumptions 6(a) and 6(b) imply that w$_{·}$ can be divided by f$_{z}$ and any generalized function can be divided by φ. Requiring that φ be in O$_{M}$ is sufficient to ensure that the model leads to equations (3) in S $^{∗}$. More detailed conditions similar to those employed in Theorem 2 would allow relaxing the infinite differentiability assumption 6(a). In particular, if γ is a characteristic function Assumption 6(a) for φ is not needed. Continuity of w$_{·}$ in 6(b) would follow by properties of convolution if either g were continuously differentiable, or f were continuous. In (b) using the same bound on growth, m, and the same V for all the functions simplifies exposition without loss of generality. The bounds could be liberal but are assumed known in the construction of estimators. The con- straint on the φ − 1 restricts the measurement error from being supersmooth and the constraint on f − 1 z does not permit fast decline to zero at infinity for the density of conditioning z ; these would be automatically satisfied if supports were bounded. Assumption (c) implies that γ and therefore ε$_{1}$ are continuous functions. Indeed an integrable function has a continuous Fourier transform, γ, and ε$_{1}$ = γφ is continuous since φ is a characteristic function and thus continuous. Assumption 6(c’) holds more generally, e.g. if g is a sum of an integrable 55