The N\(^{-1}\)-property of maps and Luzin's condition (N) (Q1916637)

We say that a function \(f:G \to R^n\), where \(G\) is an open set in \(R^n\), has the N\(^{-1}\)-property if the inverse image of a null set is a null set. The paper deals with the relation between the N\(^{-1}\)-property of functions, the maximal rank of approximate derivatives and the differentiability a.e. of superpositions of functions. It should be noted that in the English version the definition of \(\Delta(G)\) is not complete -- the property of a.e. differentiability is missing.