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Hereditary properties of the class of closed sets of uniqueness for trigonometric series

Abstract

It is shown that theσ-idealU 0 of closed sets of extended uniqueness inT is hereditarily non-Borel, i.e. every “non-trivial”σ-ideal of closed setsIU 0 is non-Borel. This implies both the result of Solovay, Kaufman that bothU 0 andU (theσ-ideal of closed sets of uniqueness) are not Borel as well as the theorem of Debs-Saint Raymond that every Borel subset ofT of extended uniqueness is of the first category. A further extension to ideals contained inU 0 is given.

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Research partially supported by NSF Grant DMS-8718847.

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Kechris, A.S. Hereditary properties of the class of closed sets of uniqueness for trigonometric series. Israel J. Math. 73, 189–198 (1991). https://doi.org/10.1007/BF02772948

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  • DOI: https://doi.org/10.1007/BF02772948

Keywords

  • Open Interval
  • Dense Subset
  • Trigonometric Series
  • Finite Union
  • Hereditary Property