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• W2069692142 abstract "The paper has two objectives. On the one hand, we study left Haar null sets, a measure-theoretic notion of smallness on Polish, not necessarily locally compact, groups. On the other hand, we introduce and investigate two classes of Polish groups which are closely related to this notion and to amenability. We show that left Haar null sets form a $sigma$-ideal and have the Steinhaus property on Polish groups which are ‘amenable at the identity’, and that they lose these two properties in the presence of appropriately embedded free subgroups. As an application we prove an automatic continuity result for universally measurable homomorphisms from inverse limits of sequences of amenable, locally compact, second countable groups to second countable groups." @default.
• W2069692142 created "2016-06-24" @default.
• W2069692142 creator A5012953076 @default.
• W2069692142 date "2006-10-13" @default.
• W2069692142 modified "2023-09-26" @default.
• W2069692142 title "AMENABILITY, FREE SUBGROUPS, AND HAAR NULL SETS IN NON-LOCALLY COMPACT GROUPS" @default.
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• W2069692142 doi "https://doi.org/10.1017/s002461150601584x" @default.
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