On a problem of Skvortsov involving the Perron integral (Q1194697)

A classical result of Saks states that the same integral is obtained whether the major and minor functions used in the Perron definition are required to be continuous or whether this requirement is omitted. Skvortsov asked if the same is true for a Perron integral defined using an abstract derivative base. The author gives a partial answer in the case of \(\mathbb{R}^ n\); the continuity condition is not completely removed, but weakened.