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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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  • 1. Arbault J., Sur l'ensemble de convergence absolue d'une série trigonométrique, Bull. Soc. Math. France 80 (1952), 253-317. MR 14:1080
  • 2. Bartoszynski T., Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), 209-213. MR 85b:03083
  • 3. Bartoszynski T. and Reclaw I., Not every $\gamma $-set is strongly meager, preprint.
  • 4. Bartoszynski T. and Scheepers M., Remarks on sets related to trigonometric series, Topology Appl. 64 (1995), 133-140. CMP 95:15
  • 5. Bary N. K., A Treatise on Trigonometric Series, Macmillan, New York, 1964.
  • 6. Bukovská Z. and Bukovský L., Adding small sets to an N-set, Proc. Amer. Math. Soc. 123 (1995), 3867-3873. MR 96b:04002
  • 7. Bukovský L., Kholshchevnikova N. N. and Repický M., Thin sets of harmonic analysis and infinite combinatorics, Real Analysis Exchange 20 (1994/95), 454-509. CMP 95:17
  • 8. van Douwen E., The integers and topology, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 111-167. MR 87f:54008
  • 9. Gerlits F. and Nagy Z., Some properties of $C(X)$, part I, Topology Appl. 14 (1982), 151-161. MR 84f:54021
  • 10. Goldstern M., Tools for your forcing construction, Set Theory of the Reals (Ramat Gan 1991), Israel Mathematical Conference Proceedings (H. Judah, ed.), vol. 6, 1993, pp. 305-360. MR 94h:03102
  • 11. Kholshchevnikova N. N., O neschetnykh R- i N-mnozhestvakh, Mat. Zametki 38 (1985), 270-277; Uncountable R- and N-sets, Math. Notes 38 (1985), 847-851. MR 87b:03115
  • 12. Reclaw I., Private communication.
  • 13. Repický M., Goldstern-Judah-Shelah preservation theorem for countable support iterations, Fund. Math. 144 (1994), 55-72. MR 95k:03082

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Additional Information

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

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