An integral on a complete metric measure space (Q1704426)

The paper under review is concerned with a generalization of the Henstock-Kurzweil integral on the real line. This is performed in the abstract framework of complete metric measure spaces endowed with a Radon measure \(\mu\) and with a family of ``cells'' \({\mathcal F}\) that satisfies the Vitali covering theorem with respect to \(\mu\). The main results are extensions of the usual descriptive characterizations of the Henstock-Kurzweil integral on the real line, in terms of \(ACG^*\) functions and in terms of variational measures.