Real Analysis Exchange

Towers and permitted trigonometric thin sets

Miroslav Repický

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In \cite{R} we introduced the notion of perfect measure zero sets and proved that every perfect measure zero set is permitted for any of the four families of trigonometric thin sets \(\\mathcal{N}\), \(\mathcal{A}\), \(\mathcal{N}_0\), and \(p\mathcal{D}\). Now we prove that the unions of less than \(\mathcal{t}\) perfect measure zero sets are permitted for the mentioned families. This strengthens a result of T. Bartoszyński and M. Scheepers \cite{BSch} saying that every set of cardinality less than \(\mathcal{t}\) is \(\mathcal{N}\)-permitted.

Article information

Real Anal. Exchange Volume 21, Number 2 (1995), 648-655.

First available in Project Euclid: 14 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 03E20: Other classical set theory (including functions, relations, and set algebra)
Secondary: 03E05: Other combinatorial set theory

\(N\)-sets \(A\)-sets \(N_0\)-sets pseudo Dirichlet sets permitted sets perfect measure zero sets


Repický, Miroslav. Towers and permitted trigonometric thin sets. Real Anal. Exchange 21 (1995), no. 2, 648--655.

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