Integration of both the derivatives with respect to \({\mathcal P}\)-paths and approximative derivatives (Q1033920)

The authors give a descriptive characteristic of the \(\mathcal P\)-primitive in terms of the generalized absolute coninuity. Using this characteristic, they then obtain some results about the relationship between the Denjoy-Khinchin integral and the Henstock \(H_{\mathcal P}\)-integral under the condition that the number sequence determining the system of \(\mathcal P\)-paths is bounded. A result about the relationship between the \(\mathcal P\)-derivative and the approximative derivative is also given.