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A family of permitted trigonometric thin sets

Author: Miroslav Repický
Journal: Proc. Amer. Math. Soc. 125 (1997), 137-144
MSC (1991): Primary 42A20; Secondary 03E05, 03E20
MathSciNet review: 1343721
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Abstract: We introduce the notion of perfectly measure zero sets and prove that every perfectly measure zero set is permitted for the families of all pseudo-Dirichlet sets, N$_{0}$-sets, A-sets and N-sets. In particular this means that these families of trigonometric thin sets are closed under adding sets of cardinality less than the additivity of Lebesgue measure.

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Miroslav Repický
Affiliation: Mathematical Institute of Slovak Academy of Sciences, Jesenná 5, 04154 Košice, Slovakia

Keywords: Trigonometric thin sets, permitted sets, perfectly measure zero sets, cardinal invariants
Received by editor(s): February 10, 1995
Received by editor(s) in revised form: June 6, 1995
Additional Notes: The work has been supported by grant 2/1224/94 of Slovenská grantová agentúra.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society