On the line contour Riemann–Stiltjes integral
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 117-126 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We introduce the notion of the line contour Riemann–Stiltjes integral and describe some of its properties. In particular, we show that this integral determines a signed measure on a plane, and specify the sufficient conditions for this measure to be countably additive.
Keywords: curve integral, Riemann–Stiltjes integral, countably additive measure.
@article{VUU_2011_3_a10,
     author = {D. L. Fedorov},
     title = {On the line contour {Riemann{\textendash}Stiltjes} integral},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {117--126},
     year = {2011},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_3_a10/}
}
TY  - JOUR
AU  - D. L. Fedorov
TI  - On the line contour Riemann–Stiltjes integral
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2011
SP  - 117
EP  - 126
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VUU_2011_3_a10/
LA  - ru
ID  - VUU_2011_3_a10
ER  - 
%0 Journal Article
%A D. L. Fedorov
%T On the line contour Riemann–Stiltjes integral
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2011
%P 117-126
%N 3
%U http://geodesic.mathdoc.fr/item/VUU_2011_3_a10/
%G ru
%F VUU_2011_3_a10
D. L. Fedorov. On the line contour Riemann–Stiltjes integral. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 3 (2011), pp. 117-126. http://geodesic.mathdoc.fr/item/VUU_2011_3_a10/

[1] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, Editorial URSS, M., 2004, 896 pp.

[2] Derr V. Ya., Teoriya funktsii deistvitelnoi peremennoi. Lektsii i uprazhneniya, Vysshaya shkola, M., 2008, 384 pp.

[3] Natanson I. P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974, 480 pp. | MR

[4] Pugachëv V. S., Lektsii po funktsionalnomu analizu, Izd-vo MAI, M., 1996, 744 pp. | MR