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Some nonabsolutely convergent integrals in the real line. (English) Zbl 0774.26003

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.

MSC:

26A39 Denjoy and Perron integrals, other special integrals
26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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