Ordinal rankings on measures annihilating thin sets
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- by Alexander S. Kechris and Russell Lyons PDF
- Trans. Amer. Math. Soc. 310 (1988), 747-758 Request permission
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.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 310 (1988), 747-758
- MSC: Primary 43A46; Secondary 03E15, 43A05, 54H05
- DOI: https://doi.org/10.1090/S0002-9947-1988-0951888-6
- MathSciNet review: 951888