On a Question by A.M. Kagan - Il'inskii, A. (Журнал математической физики, анализа, геометрии, 2010)
There is given an example of probability distribution, not having Gaussian components, such that for any two independent identically distributed random variables ξ and η with this distribution and for all a ≠ 0, b ≠ 0 the distribution of the linear form aξ + bη has Gaussian components.