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Ordinal Rankings on Measures Annihilating Thin Sets

Kechris, Alexander S. and Lyons, Russell (1988) Ordinal Rankings on Measures Annihilating Thin Sets. Transactions of the American Mathematical Society, 310 (2). pp. 747-758. ISSN 0002-9947. doi:10.2307/2000989.

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We assign a countable ordinal number to each probability measure which annihilates all H-sets. The descriptive-set theoretic structure of this assignment allows us to show that this class of measures is coanalytic non-Borel. In addition, it allows us to quantify the failure of Rajchman's conjecture. Similar results are obtained for measures annihilating Dirichlet sets.

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Additional Information:© 1988 American Mathematical Society. Received by the editors September 10, 1987. Research of the first author partially supported by NSF grant DMS8718847. The second author was partially supported by an NSF Postdoctoral Fellowship.
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NSF Postdoctoral FellowshipUNSPECIFIED
Subject Keywords:Rajchman measures, thin sets, sets of uniqueness, rank
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Other Numbering System NameOther Numbering System ID
MathSciNet ReviewMR0951888
Issue or Number:2
Classification Code:1980 Mathematics Subject Classification (1985 Revision). Primary 43A46, 03E15; Secondary 43A05, 42A63, 54H05
Record Number:CaltechAUTHORS:20130522-131009335
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Official Citation:Ordinal Rankings on Measures Annihilating Thin Sets(pp. 747-758) Alexander S. Kechris and Russell Lyons Stable URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38636
Deposited By: Ruth Sustaita
Deposited On:22 May 2013 20:30
Last Modified:09 Nov 2021 23:38

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