Growth conditions for thin sets in Vilenkin groups of bounded order

Author:
D. J. Grubb

Journal:
Proc. Amer. Math. Soc. **119** (1993), 567-571

MSC:
Primary 43A46; Secondary 42C25

MathSciNet review:
1151811

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Abstract: Let be a Vilenkin group of bounded order and a sequence of clopen subgroups of forming a base at the identity. If is a subset of , let denote the number of cosets of which intersect . If

**[1]**D. J. Grubb,*𝑈-sets in compact, 0-dimensional, metric groups*, Canad. Math. Bull.**32**(1989), no. 2, 149–155. MR**1006739**, 10.4153/CMB-1989-022-2**[2]**D. J. Grubb,*Dirichlet sets in Vilenkin groups*, Acta Math. Hungar.**62**(1993), no. 1-2, 131–135. MR**1237000**, 10.1007/BF01874224**[3]**Jean-Pierre Kahane,*A metric condition for a closed circular set to be a set of uniqueness.*, J. Approximation Theory**2**(1969), 233–236. MR**0247363****[4]**Robert Kaufman,*Kronecker sets and metric properties of 𝑀₀-sets*, Proc. Amer. Math. Soc.**36**(1972), 519–524. MR**0310540**, 10.1090/S0002-9939-1972-0310540-4

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1993-1151811-5

Article copyright:
© Copyright 1993
American Mathematical Society