Geometric cardinal invariants, maximal functions and a measure theoretic pigeonhole principle
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.
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1130335207
Digital Object Identifier: doi:10.2178/bsl/1130335207
Mathematical Reviews number (MathSciNet): MR2198711
Zentralblatt MATH identifier: 1105.03049