On the \(n\)-dimensional Perron integral defined by ordinary derivates (Q1852374)

In this note, a version of \(n\)-dimensional Perron integrals defined by ordinary (in the Saks terminology) derivatives is discussed. Continuity of major and minor functions is redundant for this version, which is proved by making use of integrals of Kurzweil-Henstock type, introduced by Mawhin. The ordinary derivative is stronger than the \(\alpha\)-regular derivative. The ordinary lower derivative is defined as the infimum of \(\alpha\)-regular lower derivatives over all \(\alpha\in (0,1)\).