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.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2017
- DOI:
- 10.48550/arXiv.1701.00281
- arXiv:
- arXiv:1701.00281
- Bibcode:
- 2017arXiv170100281P
- Keywords:
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- Mathematics - Functional Analysis;
- Mathematics - Group Theory;
- 22A05;
- 43A07
- E-Print:
- 12 pages