On classes of functions generating absolutely continuous variational measures (Q1772954)

The main result of this paper is that for a Vitali derivation basis \(\mathfrak{B}\) in \(R^m\) which satisfies \(| \partial M| =0\) and \(\text{Int\,} M \neq \emptyset\) for any \((x,M)\in \mathfrak{B}\), a function generates a \(\sigma\)-finite absolutely continuous variational measure if and only if this function belongs to \(ACG_{\delta}\)-class.