On singularity of Henstock integrable functions (Q1852334)

If \(f : [0,1]\to\mathbb R\) is Henstock--Kurzweil integrable then \(x\in[0,1]\) is a point of \textit{non-summability} (`\textit{singular point}' in the paper under review) if \(\int_I|f|\) diverges for every open interval \(x\in I\subset[0,1]\). An example shows that for each \(0<\lambda<1\) there is a Henstock--Kurzweil integrable function \(f\) such that the set of points of non-summability has measure \(\lambda\). All the results of this paper, including the definition of point of non-summability and the example, are contained in pages 147-149 of [\textit{R. L. Jeffery}, ``The theory of functions of a real variable'' (1951; Zbl 0043.27901)].