Geodesic
On the existence of continual closed $U$-set
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 76-79.

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In this work we consider a system of characters of the Vilrnkin group $G$ and study uniqueness sets for series for system of character of Vilenkin group (in other words, $U$-sets). We prove a sufficient condition for the $U$-set on the Vilenkin group and constructed continual closed $U$-set on the Vilenkin group. 
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I. S. Yurchenko. On the existence of continual closed $U$-set. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 1, pp. 76-79. http://geodesic.mathdoc.fr/item/ISU_2016_16_1_a6/

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