On amenability and groups of measurable maps

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.

12 pages; v2: minor corrections and rearrangements

References in corpus (2)

• On Følner sets in topological groups
• Continuity of convolution and SIN groups

Cited by in corpus (7)

• Equivariant concentration in topological groups
• Concentration of invariant means and dynamics of chain stabilizers in continuous geometries
• Isometry group of Borel randomizations
• Concentration of measure, classification of submeasures, and dynamics of $L_0$
• Groups without unitary representations, submeasures, and the escape property
• Topologically 2-generated groups
• Equivariant dissipation in non-archimedean groups