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Haar null and Haar meager sets: a survey and new results

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arxiv 1606.06607 v3 pith:CDAF3TWB submitted 2016-06-21 math.LO math.GNmath.GR

Márton Elekes , Donát Nagy This is my paper · ORCID
classification math.LOmath.GNmath.GR
keywords haarsetsnullresultsmeagerprovesomesurvey
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We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area. We also present several recently introduced ideas, including the notion of Haar meager sets, which are closely analogous to Haar null sets. We prove some results in a more general setting than that of the papers where they were originally proved and prove some results for Haar meager sets which were already known for Haar null sets.

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  1. Cardinal invariants of Haar null and Haar meager sets

    math.LO 2019-08 accept novelty 7.0 of 10

    For Z^omega, the four cardinal invariants of Haar null and Haar meager ideals are determined in ZFC: additivity omega_1, covering min{b,cov(N)} (respectively cov(M)), uniformity max{d,non(N)} (respectively non(M)), an...

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