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December 2005 Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle
Juris Steprāns
Bull. Symbolic Logic 11(4): 517-525 (December 2005). DOI: 10.2178/bsl/1130335207

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.

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Juris Steprāns. "Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle." Bull. Symbolic Logic 11 (4) 517 - 525, December 2005. https://doi.org/10.2178/bsl/1130335207

Information

Published: December 2005
First available in Project Euclid: 26 October 2005

zbMATH: 1105.03049
MathSciNet: MR2198711
Digital Object Identifier: 10.2178/bsl/1130335207

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.11 • No. 4 • December 2005
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