Bulletin of Symbolic Logic

Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle

Juris Steprāns

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Abstract

It is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

Article information

Source
Bull. Symbolic Logic Volume 11, Issue 4 (2005), 517-525.

Dates
First available in Project Euclid: 26 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bsl/1130335207

Digital Object Identifier
doi:10.2178/bsl/1130335207

Mathematical Reviews number (MathSciNet)
MR2198711

Zentralblatt MATH identifier
1105.03049

Citation

Steprāns, Juris. Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle. Bull. Symbolic Logic 11 (2005), no. 4, 517--525. doi:10.2178/bsl/1130335207. https://projecteuclid.org/euclid.bsl/1130335207.


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