Geodesic
The Alpha-integral of Stieltjes type
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2006), pp. 41-62

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. 
@article{VUU_2006_1_a3,
     author = {V. Ya. Derr and D. M. Kinzebulatov},
     title = {The {Alpha-integral} of {Stieltjes} type},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {41--62},
     publisher = {mathdoc},
     number = {1},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2006_1_a3/}
}
TY  - JOUR
AU  - V. Ya. Derr
AU  - D. M. Kinzebulatov
TI  - The Alpha-integral of Stieltjes type
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2006
SP  - 41
EP  - 62
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2006_1_a3/
LA  - ru
ID  - VUU_2006_1_a3
ER  - 
%0 Journal Article
%A V. Ya. Derr
%A D. M. Kinzebulatov
%T The Alpha-integral of Stieltjes type
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2006
%P 41-62
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2006_1_a3/
%G ru
%F VUU_2006_1_a3
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/