  Classical Luzin's theorem states that the measurable function of one variable
is "almost" continuous. This is not so anymore for functions of several
variables. The search of right analogue of the Luzin theorem leads to a notion
of virtually continuous functions of several variables. This probably new
notion appears implicitly in the statements like embeddings theorems and traces
theorems for Sobolev spaces. In fact, it reveals their nature as theorems about
virtual continuity. This notion is especially useful for the study and
classification of measurable functions, aswell as in some questions on
dynamical systems, polymorphisms and bistochastic measures. In this work we
recall necessary definitions and properties of admissible metrics, define
virtual continuity, describe some of applications. Detailed analysis is to be
presented in another paper.
