Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 687-698
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B. V. Levin; N. M. Timofeev. The analogue of the law of large numbers for additive functions on sparse sets. Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 687-698. http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/
@article{MZM_1975_18_5_a4,
author = {B. V. Levin and N. M. Timofeev},
title = {The analogue of the law of large numbers for additive functions on sparse sets},
journal = {Matemati\v{c}eskie zametki},
pages = {687--698},
year = {1975},
volume = {18},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/}
}
TY - JOUR
AU - B. V. Levin
AU - N. M. Timofeev
TI - The analogue of the law of large numbers for additive functions on sparse sets
JO - Matematičeskie zametki
PY - 1975
SP - 687
EP - 698
VL - 18
IS - 5
UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/
LA - ru
ID - MZM_1975_18_5_a4
ER -
%0 Journal Article
%A B. V. Levin
%A N. M. Timofeev
%T The analogue of the law of large numbers for additive functions on sparse sets
%J Matematičeskie zametki
%D 1975
%P 687-698
%V 18
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a4/
%G ru
%F MZM_1975_18_5_a4
An analog of the Turan'n–Kubilyus inequality is proved for a sufficiently wide class of sequences which contains, in particular, $a_n=f(n)$ and $a_n=f(p_n)$, where $f(n)$ is a polynomial with integral coefficients. This result helps us to obtain integral limit theorems for additive functions on the class of sequences under investigation.
