On variational measures related to some bases (Q1589711)

The variational measure \(V\) generated by an additive function and associated with the full basis of intervals is \(\sigma\)-finite whenever \(V\) is absolutely continuous with respect to the Lebesgue measure \(\lambda\) (\(\lambda(N)= 0\) implies \(V(N)= 0\)). This result was proved by the same authors few years ago. In this paper, it is extended to a certain class of differentiation bases. Under these bases, descriptive characterizations of Henstock-type integrals are given and continuity of major and minor functions of the Perron integral is also discussed.