On amenability and groups of measurable maps

Friedrich Martin Schneider; Vladimir G. Pestov

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On amenability and groups of measurable maps

Vladimir G. Pestov, Friedrich Martin Schneider

Functional Analysis · Submitted 1 Jan 2017

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely amenable.

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We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely amenable. Conversely, we prove that a topological group $G$ is amenable if $L^{0}(G)$ is.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely amenable.	result 0.99	0.95	0.61	asserted 1.00
s1	Conversely, we prove that a topological group $G$ is amenable if $L^{0}(G)$ is.	result 0.99	0.93	0.30	asserted 1.00

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Original abstract

We show that if $G$ is an amenable topological group, then the topological group $L^{0}(G)$ of strongly measurable maps from $([0,1],\lambda)$ into $G$ endowed with the topology of convergence in measure is whirly amenable, hence extremely amenable. Conversely, we prove that a topological group $G$ is amenable if $L^{0}(G)$ is.

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2 arXiv papers cite this in 2 sentences

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In recent years, the structure and dynamics of those groups has been frequently studied, for example in [ref] .

Topologically 2-generated groups · Definitions and Results · 1.00
For example, Glasner [ref] , Pestov [ref] , Pestov-Schneider [ref] , Farah-Solecki [ref] , and Sabok [ref] , studied extreme amenability for such groups.

Automorphism groups of countable structures and groups of measurable functions · Introduction · 0.96

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