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

Kechris, Alexander S. (1991) Hereditary properties of the class of closed sets of uniqueness for trigonometric series. Israel Journal of Mathematics, 73 (2). pp. 189-198. ISSN 0021-2172. https://resolver.caltech.edu/CaltechAUTHORS:20130521-093201219

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Abstract

It is shown that theσ-ideal U_0 of closed sets of extended uniqueness in T is hereditarily non-Borel, i.e. every "non-trivial" σ-ideal of closed sets I ⊆ U_0 is non-Borel. This implies both the result of Solovay, Kaufman that both U_0 and U(the σ-ideal of closed sets of uniqueness) are not Borel as well as the theorem of Debs-Saint Raymond that every Borel subset of T of extended uniqueness is of the first category. A further extension to ideals contained in U_0 is given.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF02772948DOIUNSPECIFIED
http://link.springer.com/article/10.1007/BF02772948PublisherUNSPECIFIED
Additional Information:© 1991 Springer-Verlag. Received October 3, 1989 and in revised form October 9, 1990. Research partially supported by NSF Grant DMS-8718847.
Funders:
Funding AgencyGrant Number
NSFDMS-8718847
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR1135211
Issue or Number:2
Record Number:CaltechAUTHORS:20130521-093201219
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130521-093201219
Official Citation: Hereditary properties of the class of closed sets of uniqueness for trigonometric series Alexander S. Kechris pp. 189-198
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38594
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 May 2013 17:00
Last Modified:03 Oct 2019 04:58

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