On Henstock-Dunford and Henstock-Pettis integrals (Q5936427)

In this note, Harnack extension theorems and convergence theorems are proved for Henstock-Pettis and Henstock-Dunford integrals. Weakly controlled convergence theorems are proved for Banach spaces \(X\), which are weakly sequentially complete or reflexive or the unit ball of \(X^*\) is \(\text{weak}^*\) sequentially compact. They are proved by means of the category argument, using Romanovskij's theorem [see ``The theory of the Denjoy integral and some applications'' (1978; Zbl 0471.26005) by \textit{V. G. Chelidze} and \textit{A. G. Dzhvarshejshvili}].