the function r − 1 n I ( B$_{n}$ ) exp (Λ( ζ )) ψ ( ζ ) is bounded . It is then sufficient to find B$_{n}$ such that r − 1 n I ( B$_{n}$ ) exp (Λ( ζ )) is bounded (by possibly a polynomial), thus it is sufficient that sup B n | exp (Λ( ζ )) r − 1 n | be bounded. This will hold if exp ( ¯ B k n ) < r$_{n}$, ¯ B k n < ln r$_{n}$. ■ Of course an even slower growth for spectral cut-off would result from Λ that grows faster than a polynomial. The consequence of the slow growth of the support is usually a correspondingly slow rate of convergence for φ − 1 u ε$_{n}$I ( B$_{n}$ ) . Additional conditions (as in function spaces) are needed for the regularized estimators to converge to the true γ . It may be advantageous to focus on lower frequency components and ignore the contribution from high frequencies when the features of interest depend on the contribution at low frequency. Working in spaces of generalized functions extends the results on nonpara- metric identification and well-posedness for a wide class of models. Here identification in deconvolution is extended to generalized densities in the class of all distributions from the usually considered classes of integrable den- sity functions. In regression with Berkson error nonparametric identification in S ∗ holds for functions of polynomial growth, extending the usual results obtained in L$_{1}$ ; a similar extension applies to regression with measurement error and Berkson type measurement; this allows to consider binary choice 6 Concluding remarks 52