A note on a Pettis-Kurzweil-Henstock type integral in Riesz spaces. (Q595856)

Let \(R\) be a Dedekind complete Riesz space such that the space \(R^*\) of its order continuous functionals separates the points of \(R\). Let \(X\) be a Hausdorff compact topological space and \(f: X\to R\). In this paper, a Pettis-Kurzweil-Henstock type integral of \(f\) on a compact subset is defined. The connection between improper integrals and integrals on compact subsets is discussed and some convergence theorems are also proved.