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Lemma 2 and thus converge to zero. Therefore, γ$_{n}$ − γ = ( ε$_{n}$ − ε ) φ − 1 → 0 in S $^{∗}$. 

By continuity in S ∗ of the inverse Fourier transform the limit 

in S ∗ follows. 

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If the measurement error model holds conditionally on some d$_{c}$ -dimensional x$_{c}$ assume that the all the distribution functions are defined on R d × R d$_{c}$ as F ( · , x$_{c}$ ) . For any generalized function b on R $^{d$_{x}$}$× R d$_{c}$ the partial Fourier trans- form F t$_{|}$$_{x}$$_{c}$ is defined as follows: for ψ ( x, x$_{c}$ ) ∈ S with x ∈ R $^{d$_{x}$}$, x$_{c}$ ∈ R d$_{c}$ define F t$_{|}$$_{x}$$_{c}$ ( ψ ) ( s, x$_{c}$ ) ∈ S by ∫ e ix $^{$^{T}$s}$ψ ( x, x$_{c}$ ) dx, then ( F t$_{|}$$_{x}$$_{c}$b, ψ ) = ( b, F t$_{|}$$_{x}$$_{c}$ ( ψ ) ) . Consider the following possibilities: 1. the generalized functions γ, φ, ε de- note now the partial Fourier transforms or the distribution functions; 2. instead of distribution functions consider generalized density functions and denote by γ, φ, ε the corresponding partial Fourier transforms; 3. assume con- tinuous differentiability of the probability distribution functions with respect to x$_{c}$ and consider conditional probability or, correspondingly, conditional generalized densities; additional conditions will be needed to make sure that dividing by the density of x$_{c}$ is possible in S $^{∗}$. In all these cases (15) holds. To avoid imposing extra constraints here examine case 2. For deconvolution φ is assumed known and often φ does not vary with x$_{c}$. The conditions of Lemma 2 may not apply as the functions ε, ε$_{n}$ may no longer be continuous, 

