Decomposition of Derivatives in Several Variables and the Class [Δ′]

AbstractA decomposition of a real functionfof one variable is a system of closed setsANand derivativesvNsuch that ⋃N=1AN=Randf=vNonAN. It is known that Peano derivatives and approximate derivatives have decompositions. We extend the notion of decomposition to functions ofmvariables and provem-dimensional analogs of these results. We also show that them-dimensional approximate derivative is Baire 1