Izvestiya. Mathematics, Tome 23 (1984) no. 3, pp. 431-447
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I. N. Blinov. On the absence of exact means for some bounded functions. Izvestiya. Mathematics, Tome 23 (1984) no. 3, pp. 431-447. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a1/
@article{IM2_1984_23_3_a1,
author = {I. N. Blinov},
title = {On the absence of exact means for some bounded functions},
journal = {Izvestiya. Mathematics},
pages = {431--447},
year = {1984},
volume = {23},
number = {3},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a1/}
}
TY - JOUR
AU - I. N. Blinov
TI - On the absence of exact means for some bounded functions
JO - Izvestiya. Mathematics
PY - 1984
SP - 431
EP - 447
VL - 23
IS - 3
UR - http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a1/
LA - en
ID - IM2_1984_23_3_a1
ER -
%0 Journal Article
%A I. N. Blinov
%T On the absence of exact means for some bounded functions
%J Izvestiya. Mathematics
%D 1984
%P 431-447
%V 23
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a1/
%G en
%F IM2_1984_23_3_a1
It is shown that there exist almost periodic functions $f(t)$ such that the function $$ \varphi(t)=\frac1{c+\int^t_0f(t)\,dt} $$ is bounded but does not have an exact mean value. This fact implies that there are first-order Bernoulli differential equations with almost periodic coefficients such that some bounded solutions do not have exact mean values. Bibliography: 2 titles.
