Geodesic
General integration and extensions. I
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 961-981

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A general concept of integral is presented in the form given by S. Saks in his famous book Theory of the Integral. A special subclass of integrals is introduced in such a way that the classical integrals (Newton, Riemann, Lebesgue, Perron, Kurzweil-Henstock\dots ) belong to it. \endgraf A general approach to extensions is presented. The Cauchy and Harnack extensions are introduced for general integrals. The general results give, as a specimen, the Kurzweil-Henstock integration in the form of the extension of the Lebesgue integral.
A general concept of integral is presented in the form given by S. Saks in his famous book Theory of the Integral. A special subclass of integrals is introduced in such a way that the classical integrals (Newton, Riemann, Lebesgue, Perron, Kurzweil-Henstock\dots ) belong to it. \endgraf A general approach to extensions is presented. The Cauchy and Harnack extensions are introduced for general integrals. The general results give, as a specimen, the Kurzweil-Henstock integration in the form of the extension of the Lebesgue integral.
Classification : 26A39, 26A42
Keywords: abstract integration; extension of integral; Kurzweil-Henstock integration 
Schwabik, Štefan. General integration and extensions. I. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 4, pp. 961-981. http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a6/
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     title = {General integration and extensions. {I}},
     journal = {Czechoslovak Mathematical Journal},
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     zbl = {1224.26030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_4_a6/}
}
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