Naively Haar null sets in Polish groups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Elekes, Marton^1,2  Vidnyanszky, Zoltan¹ 

[1] Hungarian Acad Sci, Atfred Renyi Inst Math, POB 127, H-1364 Budapest, Hungary

[2] Eotvos Lorand Univ, Dept Anal, Pazmany Ps 1-c, H-1117 Budapest, Hungary

关键词: Polish groups;    Haar null;    Christensen;    Shy;    Universally measurable;    Problem FC;   

DOI  :  10.1016/j.jmaa.2016.08.033

来源: Elsevier

【 摘 要 】

Let (G,.) be a Polish group. We say that a set X subset of G is Haar null if there exists a universally measurable set U superset of X and a Borel probability measure mu such that for every g,h epsilon G we have mu,(gUh) = 0. We call a set X naively Haar null if there exists a Borel probability measure A such that for every g, h epsilon G we have mu(gXh) = 0. Generalizing a result of Elekes and Steprans, 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. (C) 2016 Published by Elsevier Inc.

【 授权许可】

Free