The Denjoy-type definition of \(B\)-integral (Q2721794)

Let \(B\) be a collection of Vitali covers of an interval in the \(n\)-dimensional space with filtering and complete properties, but without partition property. Then the multidimensional Henstock variational integral can be defined using \(B\). In this short note, a corresponding Denjoy integral is given. However, intervals used in the integral are regular. Since the regularity of an interval is not a hereditary property, the integrability over an interval does not imply that over all subintervals.