Geodesic
Two remarks on properties of functions of bounded variation
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 3, pp. 7-16
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In terms of variations, a sufficient condition for the uniform convergence of sequences of continuous functions is proved. Using this result, we obtain an addition to the classical Helly theorem on the selection of convergent sequences of functions with uniformly bounded variations in the case when the limit function is continuous. Also, by using an example we show that the condition of continuous differentiability of a function, ensuring the differentiability of its variation with the variable upper limit, is in a certain sense sharp.
Mots-clés : variation, uniform convergence
Keywords: function of bounded variation, modulus of continuity, Helly's theorem, Stolz's theorem. 
@article{VSGU_2024_30_3_a0,
     author = {S. V. Astashkin and V. M. Ershov},
     title = {Two remarks on properties of functions of bounded variation},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {7--16},
     year = {2024},
     volume = {30},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2024_30_3_a0/}
}
TY  - JOUR
AU  - S. V. Astashkin
AU  - V. M. Ershov
TI  - Two remarks on properties of functions of bounded variation
JO  - Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
PY  - 2024
SP  - 7
EP  - 16
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VSGU_2024_30_3_a0/
LA  - ru
ID  - VSGU_2024_30_3_a0
ER  - 
%0 Journal Article
%A S. V. Astashkin
%A V. M. Ershov
%T Two remarks on properties of functions of bounded variation
%J Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ
%D 2024
%P 7-16
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/VSGU_2024_30_3_a0/
%G ru
%F VSGU_2024_30_3_a0
S. V. Astashkin; V. M. Ershov. Two remarks on properties of functions of bounded variation. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, Tome 30 (2024) no. 3, pp. 7-16. http://geodesic.mathdoc.fr/item/VSGU_2024_30_3_a0/

[1] Bogachev V.I., Smolyanov O.G., Deistvitelnyi i funktsionalnyi analiz: universitetskii kurs, NITs “Regulyarnaya i khaoticheskaya dinamika”, M.–Izhevsk, 2011, 728 pp. https://djvu.online/file/J45IxweiiQHOT?ysclid=m1erhtogan399934303

[2] Gorodetskii V.V., Nagnibida N.I., Nastasiev P.P., Metody resheniya zadach po funktsionalnomu analizu, LIBROKOM, M., 2010, 479 pp. https://djvu.online/file/rMxu2zCznQGSW?ysclid=m1f3l7qh3k850744665

[3] Kolmogorov A.N., Fomin S.V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976, 542 pp. https://djvu.online/file/acB4ODGXeJeSf?ysclid=m1f3rqwfjj688702689 | MR

[4] Natanson I.P., Teoriya funktsii veschestvennoi peremennoi, Nauka, M., 1974, 480 pp. https://djvu.online/file/KO7DQP52iL3oh?ysclid=m1f3v42p8s44016586

[5] Fikhtengolts G.M., Kurs differentsialnogo i integralnogo ischisleniya, v. I, Nauka, M., 1962, 616 pp. https://djvu.online/file/x6N9RDsAtAL7X?ysclid=m1f3yq51dy652360573