Short notes

Union of $U_r$-sets for the system of characters of the group of $p$-adic numbers

T. D. Kozlovskaya

Moscow State Technological University "Stankin"

Abstract: 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.

Key words: group of $p$-adic intergers, zero-dimensional group, characters of a group, Vilenkin–Dzhafarli system, $U_r$-sets.

UDC: 517.518.43

Received: 27.06.2018

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