Description of the limit set of Henstock-Kurzweil integral sums of vector-valued functions (Q743185)

Let \(X\) be a separable Banach space and \(f:[0,1]\to X\) be an \(i\)-bounded function. The following statement is a synthesis of the main results in the paper. Theorem. Under these conditions, we have {\parindent=6mm \begin{itemize}\item[(i)] \(I_{HK}(f)=V(f)\); hence, \(I_{HK}(f)\) is nonempty convex; \item[(ii)] there exists a multifunction \(Q:[0,1]\to \text{cl}(X)\) such that \(I_{HK}(f|_J)=\overline{(B)\int_J Qd\lambda}\) for each interval \(J:=[a,b]\) of \([0,1]\). \end{itemize}} Some other aspects involving the set \(I_{HK}(f)\) are also discussed.