Decomposition of Derivatives in Several Variables and the ClasswD9x

A decomposition of a real function f of one variable is a system of closed sets ANand derivatives ¨Nsuch that DNs1 ANsR and fs¨Non AN. It is known that Peano derivatives and approximate derivatives have decompositions. We extend the notion of decomposition to functions of m variables and prove m-dimensional analogs of these results. We also show that the m-dimensional approximate derivative is Baire 1.