Behavioral sciences and auto-transformations of functions

The two goals of the present article are: 1) To define transformations (named here as auto-transformations) of the probability density functions of random variables (or other functions) into similar functions having smaller sizes of their domains. 2) To research and outline basic features of these transformations. In particular, auto-transformations from infinite to finite domains are analyzed. The goals are caused by the well-known problems of behavioral sciences.