ABSTRACT
In various questions of analysis, we often need to consider some nontrivial restrictions of a given function (e.g., acting from R into R), which have nice additional descriptive properties. In general, these properties do not hold for the original function. In order to illustrate this, let us recall two widely known statements from the theory of real functions. The first of them is the classical theorem of Luzin concerning the structure of an arbitrary Lebesgue measurable function acting fromR intoR. Undoubtedly, this theorem plays the most fundamental role in real analysis and measure theory.
