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Abstract We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with distributional values everywhere or nearly everywhere.
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(Rozprawy Mat.), 52 [Google Scholar] and is far from being obvious. In the same paper, the authors show why this definition is to be preferred to various other possibilities.Dissertationes math