Bongiorno, Benedetto; Giertz, Magnus; Pfeffer, Washek F. Some nonabsolutely convergent integrals in the real line. (English) Zbl 0774.26003 Boll. Unione Mat. Ital., VII. Ser. B 6, No. 2, 371-402 (1992). The paper is devoted to the detailed analysis of the properties of the one-dimensional version of some integrals of Riemann type introduced in recent years to prove Stokes theorems with minimal differentiability conditions. It is shown that those integrals are intermediate between the Lebesgue and the Denjoy-Perron integrals. For the reader’s convenience, the one-dimensional theory is reconstructed in the paper, which requires only some familiarity with the Kurzweil-Henstock integral. Reviewer: J.Mawhin (Louvain-La-Neuve) Cited in 1 ReviewCited in 2 Documents MSC: 26A39 Denjoy and Perron integrals, other special integrals 26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) Keywords:de Giorgi perimeter; BV sets; nonabsolutely convergent integrals; integrals of Riemann type; Stokes theorems; Kurzweil-Henstock integral PDFBibTeX XMLCite \textit{B. Bongiorno} et al., Boll. Unione Mat. Ital., VII. Ser., B 6, No. 2, 371--402 (1992; Zbl 0774.26003)