The following theorem is proved: the union of countably many closed U_r-sets (r > 2) for the Vilenkin-Dzhafarli system is again a U_r-set for this system.

中文翻译：

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p-adic整数组的字符系统的U r集的并集

证明以下定理：Vilenkin-Dzhafarli系统的无数个闭合U _r集（r > 2）的并集再次是该系统的U _r集。