The multidimensional Luzin theorem (Q2465184)

Using the \textit{G. Alberti} theorem [J. Funct. Anal. 100, No. 1, 110--118 (1991; Zbl 0752.46025)] and Luzin's argument, the authors give a multidimensional generalization of the following Luzin theorem. For every measurable \(f: \mathbb{R}\to\mathbb{R}\) there exists a function \(F: \mathbb{R}\to \mathbb{R}\) such that \(F'= f\) a.e. as an application they generalize the Saks-Howard-Pfeffer Luzin's type multidimensional result to \(m\)-charges [\textit{E. J. Howard} and \textit{W. F. Pfeffer}, Proc. Am. Math. Soc. 132, No. 3, 857--863 (2004; Zbl 1037.28001)].