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Covering theorems for uniqueness and extended uniqueness sets

Kechris, Alexander S. and Louveau, Alain (1990) Covering theorems for uniqueness and extended uniqueness sets. Colloquium Mathematicum, 59 (1). pp. 63-79. ISSN 0010-1354.

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A covering theorem for a class of sets C asserts that every set in C can be covered by a countable union of sets in some (somehow simpler) class C. In the theory of sets of uniqueness on the unit circle T the first result of this kind is Piatetski-Shapiro's theorem in [PS], which states that every closed set of uniqueness can be covered by countably many closed sets in the class U'_1, consisting of those closed sets E ⊆ T for which there exists a sequence of functions in A(T), vanishing on E, which converges to the function 1 in the weak^*-topology.

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Additional Information:© 1990 Polish Academy of Sciences. Reçu par la Redaction le 20.12.1988. Research partially supported by NSF Grant.
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MathSciNet ReviewMR1078293
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Official Citation:Covering theorems for uniqueness and extended uniqueness sets Alexander S. Kechris, Alain Louveau Colloq. Math. 59 (1990), 63-79
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38901
Deposited By: Ruth Sustaita
Deposited On:12 Jun 2013 16:07
Last Modified:03 Oct 2019 05:01

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