Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4613810 | Journal of Mathematical Analysis and Applications | 2017 | 8 Pages |
Abstract
Let (G,⋅)(G,⋅) be a Polish group. We say that a set X⊂GX⊂G is Haar null if there exists a universally measurable set U⊃XU⊃X and a Borel probability measure μ such that for every g,h∈Gg,h∈G we have μ(gUh)=0μ(gUh)=0. We call a set X naively Haar null if there exists a Borel probability measure μ such that for every g,h∈Gg,h∈G we have μ(gXh)=0μ(gXh)=0. Generalizing a result of Elekes and Steprāns, which answers the first part of Problem FC from Fremlin's list, we prove that in every abelian Polish group there exists a naively Haar null set that is not Haar null.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Márton Elekes, Zoltán Vidnyánszky,