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Ordinal rankings on measures annihilating thin sets

Authors: Alexander S. Kechris and Russell Lyons
Journal: Trans. Amer. Math. Soc. 310 (1988), 747-758
MSC: Primary 43A46; Secondary 03E15, 43A05, 54H05
MathSciNet review: 951888
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Abstract: 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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Keywords: Rajchman measures, thin sets, sets of uniqueness, rank
Article copyright: © Copyright 1988 American Mathematical Society

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