Further, the issue of regularizattion is discussed. Assumption 1. The generalized functions g, f, w$_{1}$ and w$_{2}$$_{k}$, k = 1 , ..., d, are in the generalized function space S ′ and are related by (6) . Any generalized density functions are generalized derivatives of the dis- tribution function and belong to S $^{′}$, convolution equations are defined. For a ordinary function, b, e.g. a regression function of example 2 to belong to S ′ it is sufficient that it belong to some class of functions on R $^{d}$, Φ( m, V ) (with m a vector of integers, V a positive constant) where b ∈ Φ( m, V ) if 2 The identification result Thus if e.g. b grows no faster than a polynomial, it is in S $^{′}$, so that the analysis here applies to binary choice and polynomial regression. Convolutions with generalized functions from some classes are defined for such functions (as discussed in Zinde-Walsh, 2010). For conditional density of Example 3 some extra assumptions on the joint density of the regressors are required. Consider now Fourier transforms ( F t ) : γ = F t ( g ); φ = F t ( f ); ε$_{.}$ = F t ( w$_{.}$ ) . ∫ Π ( (1 + t 2 $_{i}$) − $^{1}$) m i | b ( t ) | dt < V < ∞ . (7) Assumption 2 . Either φ or γ is a continuous function such that it satisfies (7) . 7