Absolutely continuous functions of several variables and diffeomorphisms - Hencl, Stanislav; Malý, Jan (Open mathematics (Warsaw, Poland), 2003)
In [4], a class of absolutely continuous functions of d-variables, motivated by applications to change of variables in an integral, has been introduced. The main result of this paper states that absolutely continuous functions in the sense of [4] are not stable under diffeomorphisms. We also show an example of a function which is absolutely continuous with respect cubes but not with respect to balls.