and polynomial regression models. Also, identification in models with sum- of-peaks regression function that cannot be represented in function spaces is included. Well-posedness results in S ∗ also extend the results in the lit- erature provided in function spaces; well-posedness of deconvolution holds as long as the characteristic function of the error distribution does not go to zero at infinity too fast (as e.g. super-smooth) and a similar condition provides well-posedness in the other models considered here. Further investigation of the properties of estimators in spaces of general- ized functions requires deriving the generalized limit process for the function being estimated and investigating when it can be described as a generalized Gaussian process. A generalized Gaussian limit process holds for kernel esti- mator of the generalized density function (Zinde-Walsh, 2008). Determining the properties of inference based on the limit process for generalized ran- dom functions requires both further theoretical development and simulations evidence. [1] An, Y, and Y. Hu (2012) Well-posedness of measurement error models for self-reported data, Journal of Econometrics, vol. 168 (2012), pp. 259- 269. [2] Ben-Moshe, D. (2012) Identification of Dependent Multidimensional Un- observed Variables in a System of Linear Equations, working paper, 53 References