Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 42-46
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T. D. Kozlovskaya. Union of $U_r$-sets for the system of characters of the group of $p$-adic numbers. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 42-46. http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a5/
@article{VMUMM_2019_4_a5,
author = {T. D. Kozlovskaya},
title = {Union of $U_r$-sets for the system of characters of the group of $p$-adic numbers},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {42--46},
year = {2019},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a5/}
}
TY - JOUR
AU - T. D. Kozlovskaya
TI - Union of $U_r$-sets for the system of characters of the group of $p$-adic numbers
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 2019
SP - 42
EP - 46
IS - 4
UR - http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a5/
LA - ru
ID - VMUMM_2019_4_a5
ER -
%0 Journal Article
%A T. D. Kozlovskaya
%T Union of $U_r$-sets for the system of characters of the group of $p$-adic numbers
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 42-46
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a5/
%G ru
%F VMUMM_2019_4_a5
The following theorem is proved: the union of countable many closed $U_{r}$-sets ($r>2$) for the Vilenkin–Dzhafarli system is again a $U_{r}$-set for this system.
[1] Agaev G. N., Vilenkin N. Ya., Dzhafarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskii analiz na nul-mernykh gruppakh, Elm, Baku, 1981 | MR
[2] Kozlovskaya T. D., “Ob $U_{p}$-mnozhestvakh dlya sistemy funktsii Uolsha”, Vestnik MGTU “Stankin”, 2012, no. 1(18), 85–88
[3] Skvortsov V. A., Tulone F., “Kurzweil–Henstock type integral on zero-dimensional group and some of its applications”, Czechoslovak Math. J., 58 (2008), 1167–1183 | DOI | MR | Zbl
[4] Skvortsov V. A., “On $M_{0}$-sets for series with respect to characters of compact zero-dimensional group”, Tatra Mt. Math. Publ., 62 (2014), 165–174 | MR
[5] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR