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. doi:10.1007/BF02772948. 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 | |||||||||
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| Additional Information: | © 1991 Springer-Verlag. Received October 3, 1989 and in revised form October 9, 1990. Research partially supported by NSF Grant DMS-8718847. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1007/BF02772948 | |||||||||
| 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: | 09 Nov 2021 23:38 |
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