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On singularity of Henstock integrable functions. (English) Zbl 1015.26016
If $$f : [0,1]\to\mathbb R$$ is Henstock–Kurzweil integrable then $$x\in[0,1]$$ is a point of non-summability (‘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 [R. L. Jeffery, “The theory of functions of a real variable” (1951; Zbl 0043.27901)].

##### MSC:
 26A39 Denjoy and Perron integrals, other special integrals