A generalized Henstock integral (Q1766425)

A specific integration based on the concept of \(\delta\)-fine tagged \(k\)-partitions is defined for functions \(U:[a,b]^{k=1} \to \mathbb R^n\) in the flavor of Henstock-Kurzweil integration. The resulting integral is called the \(GH_k\) integral. If \(k=1\) then the \(GH_1\) integral coincides with the integral described in the reviewers book ``Generalized ordinary differential equations'' (1992; Zbl 0781.34003). Basic results for the \(GH_k\) integral are presented (Saks-Henstock lemma, Cauchy extension) and in the introduction other similar concepts of integration are discussed.