Maximal Functions and the Additivity of Various Families of Null Sets
نویسنده
چکیده
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 are obtained for circles in the plane as well as other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain maximal operators and a measure theoretic pigeonhole principle.
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