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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

Miroslav Repický
Affiliation: Mathematical Institute of Slovak Academy of Sciences, Jesenná 5, 04154 Košice, Slovakia
Email: repicky@kosice.upjs.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03516-8
PII: S 0002-9939(97)03516-8
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