Typically the convolution equation is written for density functions when the distribution function is absolutely continuous. The usual approach to possible non-existence of density avoids considering the convolution and focuses on the characteristic functions. Since density always exists as a generalized function and convolution for such gen- eralized functions is always defined it is possible to write convolution equa- tions in S ∗ for any distributions in model 1. The error distribution (and thus generalized density f$_{u}$ ) is assumed known thus the solution can be obtained by ”deconvolution” (Carrol et al (2006), Meister (2009), the review of Chen et al (2011) and papers by Fan (1991), Carrasco and Florens(2010) among others). For Berkson error the convolution equation is also well-known. Berkson error of measurement arises when the measurement is somehow controlled and the error is caused by independent factors, e.g. amount of fertilizer applied is given but the absorption into soil is partially determined by factors independent of that, or students’ grade distribution in a course is given in advance, or distribution of categories for evaluation of grant proposals is determined by the granting agency. The properties of Berkson error are very different from that of classical error of measurement, e.g. it does not lead to 16 2. The Berkson error model. f$_{x}$ ∗ ∗ f$_{u}$ = f$_{z}$