On the n-Dimensional Perron Integral Defined by Ordinary Derivates

Abstract

We introduce an $n$-dimensional Perron integral defined in terms of ordinary (in the Saks terminology) derivates. We prove that we get an equivalent definition of this integral if in the definition we use only continuous major and minor functions. We also prove that this integral is equivalent to a version of the Kurzweil-Henstock integral defined by Mawhin.