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Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

Published online by Cambridge University Press:  15 January 2014

Juris Steprāns
Juris Steprāns*
Affiliation:
Department of Mathematics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada. E-mail: steprans@yorku.ca
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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.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 11 , Issue 4 , December 2005 , pp. 517 - 525
Copyright
Copyright © Association for Symbolic Logic 2005

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References

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