Geodesic
The Alpha-integral of Stieltjes type
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 41-62 
V. Ya. Derr; D. M. Kinzebulatov. The Alpha-integral of Stieltjes type. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 41-62. http://geodesic.mathdoc.fr/item/VUU_2006_1_a3/
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     title = {The {Alpha-integral} of {Stieltjes} type},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The equivalence classes of regulated functions, which differ only on the points of discontinuity, are considered. On these classes the integral of Riemann–Stieltjes is extenced; one modification of Perron–Stieltjes integral (called alpha-integral) is introduced for them. The integration by parts theorem, the substitution theorem, the change of order of integration theorem, the convergence theorems for these integrals are proved.