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

 

Adding small sets to an $ {\bf N}$-set


Authors: Zuzana Bukovská and Lev Bukovský
Journal: Proc. Amer. Math. Soc. 123 (1995), 3867-3873
MSC: Primary 04A15; Secondary 03E05, 03E15, 03E50, 04A20, 42A99, 43A46
MathSciNet review: 1285977
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Abstract: Pseudo Dirichlet and N-sets are small sets of reals defined in the theory of trigonometric series. We prove that by adding a set of cardinality smaller than $ \mathfrak{p}$ to an N-set one obtains again an N-set. This is a strengthening of Arbault-Erdös' theorem about adding countable sets to N-sets. A similar result holds true for pseudo Dirichlet sets.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1285977-5
PII: S 0002-9939(1995)1285977-5
Keywords: Trigonometric series, N-set, pseudo Dirichlet set, $ \mathfrak{p}$
Article copyright: © Copyright 1995 American Mathematical Society