Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 815-824
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N. B. Pogosyan. Systems of functions which are complete in measure. Matematičeskie zametki, Tome 18 (1975) no. 6, pp. 815-824. http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a2/
@article{MZM_1975_18_6_a2,
author = {N. B. Pogosyan},
title = {Systems of functions which are complete in measure},
journal = {Matemati\v{c}eskie zametki},
pages = {815--824},
year = {1975},
volume = {18},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a2/}
}
TY - JOUR
AU - N. B. Pogosyan
TI - Systems of functions which are complete in measure
JO - Matematičeskie zametki
PY - 1975
SP - 815
EP - 824
VL - 18
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a2/
LA - ru
ID - MZM_1975_18_6_a2
ER -
%0 Journal Article
%A N. B. Pogosyan
%T Systems of functions which are complete in measure
%J Matematičeskie zametki
%D 1975
%P 815-824
%V 18
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1975_18_6_a2/
%G ru
%F MZM_1975_18_6_a2
In this note it is proved that if a complete orthonormal system $\{\varphi_n\}$ in $L_2[0,1]$ contains a subsystem $\{\varphi_{n_k}\}$ of a lacunary order $p>2$, then for some bounded measurable function $h(x)$ the system $\{h(x)\varphi_n(x)\}_{n\ne n_k}$ is complete in $L_2[0,1]$.
