Geodesic
A new characterization of Riemann-integrable functions
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 73-83
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we describe Riemann-integrable functions with the help of a new class of uniform functions. This description allows us to uncover the “countable” nature of the relation between the space of Riemann-integrable functions and the space of continuous functions. The argumentation is performed for any given topological space $T$ with limited Radon measure $\mu$ the support of which coincides with $T$. 
@article{FPM_2004_10_3_a3,
     author = {V. K. Zakharov and A. A. Seredinskii},
     title = {A~new characterization of {Riemann-integrable} functions},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {73--83},
     year = {2004},
     volume = {10},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a3/}
}
TY  - JOUR
AU  - V. K. Zakharov
AU  - A. A. Seredinskii
TI  - A new characterization of Riemann-integrable functions
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2004
SP  - 73
EP  - 83
VL  - 10
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a3/
LA  - ru
ID  - FPM_2004_10_3_a3
ER  - 
%0 Journal Article
%A V. K. Zakharov
%A A. A. Seredinskii
%T A new characterization of Riemann-integrable functions
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2004
%P 73-83
%V 10
%N 3
%U http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a3/
%G ru
%F FPM_2004_10_3_a3
V. K. Zakharov; A. A. Seredinskii. A new characterization of Riemann-integrable functions. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 3, pp. 73-83. http://geodesic.mathdoc.fr/item/FPM_2004_10_3_a3/

[1] Vulikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Fizmatgiz, M., 1961 | MR

[2] Zakharov V. K., “Svyaz mezhdu polnym koltsom chastnykh koltsa nepreryvnykh funktsii, regulyarnym popolneniem i rasshireniyami Khausdorfa–Serpinskogo”, Uspekhi mat. nauk, 45:6 (1990), 133–134 | MR | Zbl

[3] Zakharov V. K., “Schetno-delimoe rasshirenie i rasshirenie Bera koltsa i banakhovoi algebry nepreryvnykh funktsii kak delimaya obolochka”, Algebra i analiz, 5:6 (1993), 121–138 | MR

[4] Lebesgue H., Leçons sur l'intégration et la recherche des fonctions primitives, Gauthier-Villars, Paris, 1904 | Zbl

[5] Vitali G., “Sulla integrabilità delle funzioni”, Ist. Lombardo Accad. Sci. Lett. Rend. (2), 37 (1904), 69–73 | Zbl

[6] Zakharov V. K., “Alexandrovian cover and Sierpin'skian extension”, Studia Sci. Math. Hungar., 24 (1989), 93–117 | MR | Zbl