The \(H\)-integral is a nonabsolute integral defined by taking Riemann sums over a partition of a metric space. The partition is constructed using scalloped balls. See [\textit{N. W. Leng} and \textit{L. P. Yee}, Bull. Lond. Math. Soc. 32, No. 1, 34--38 (2000; Zbl 1028.26005)] for details. In the paper under review the author proves a type of Radon-Nikodým result. Theorem 17: Let \(F\) be an elementary-set function which is finitely additive and strongly \(ACG_\Delta\) on \(E\) such that its derived sequence \(\{F_i\}\) on \(\{X_i\}\) satisfies the (\(WL\))-condition on \(\{X_i\}\). Then there exists a function \(f\) which is \(H\)-integrable on \(E\) such that for any elementary subset \(E_0\) of \(E\), we have \[ F(E_0)=(H)\int_{E_0}f. \] Moreover, the function \(f\) is unique in the sense that if \(g\) is a \(H\)-integrable function on \(E\) for which the above equation holds, then \(f=g\) almost everywhere on \({\overline E}\). Elementary sets are finite unions of scalloped balls. The definition of \(ACG_\Delta\) (a generalised type of absolute continuity) is given in the paper. The \((WL)\) condition is a type of Saks-Henstock lemma. A descriptive definition of the \(H\)-integral is also proven. It should be noted that in [\textit{N. W. Leng} and \textit{L. P. Yee} (loc. cit.)] it is stated that generalised intervals are connected. However, if in \(\mathbb R^2\) we have \(X=B((0,0),1)\), \(Y=B((1/2, 0),1)\) and \(Z=B((2,0),\sqrt{5})\) then \(X\), \(Y\) and \(Z\) are closed balls in \(H_1\), which consists of closed or scalloped balls. The intersection of \(X\setminus Y\) and \(Z\) is not connected but is in \(H_2\), which is the set of generalised intervals, or finite intersections of sets in \(H_1\).