Recall that for two functions, f and g convolution f ∗ g is defined by this expression is not always defined. A similar expression (with some abuse of notation since generalized functions are not defined pointwise) may hold for generalized functions in S $^{∗}$; similarly, it is not always defined. With As- sumption 1 for the models considered here we show that convolution equa- tions given in the Tables below hold in S $^{∗}$. Table 1. Measurement error models: 1. Classical measurement error; 2. Berkson measurement error; 3. Classical measurement error with additional observation (with zero conditional mean error); 4., 4a. Classical error with additional observation (full independence). 13 ( f ∗ g ) ( x ) = ∫ f ( w ) g ( x − w ) dw ;