Real Analysis Exchange

Towers and permitted trigonometric thin sets

Miroslav Repický

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694093

Mathematical Reviews number (MathSciNet)
MR1407277

Zentralblatt MATH identifier
0879.42004

Subjects
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

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

Citation

Repický, Miroslav. Towers and permitted trigonometric thin sets. Real Anal. Exchange 21 (1995), no. 2, 648--655.https://projecteuclid.org/euclid.rae/1339694093


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