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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Kronecker sets and metric properties of $ M\sb{0}$-sets


Author: Robert Kaufman
Journal: Proc. Amer. Math. Soc. 36 (1972), 519-524
MSC: Primary 42A72; Secondary 43A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0310540-4
MathSciNet review: 0310540
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Abstract: A method for constructing both sets of multiplicity and Kronecker sets within a given set of multiplicity is derived from the work of Ivashev-Musatov; it is shown that the Hausdorff measures and other measures are essentially distinct. Finally, an improvement of a theorem of Salem is obtained, using Pyateckiĭ-Shapiro's theorem on non-M sets.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0310540-4
Keywords: K-set, $ {M_0}$-set, M-set, uniform distribution, Diophantine approximation, Fourier transform
Article copyright: © Copyright 1972 American Mathematical Society