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Topological and measurewise amenability for locally compact groupoids
Abstract
We prove the equivalence of topological and measurewise amenability for σ-compact locally compact groupoids with a Hausdorff unit space and a continuous Haar system. This in particular includes the second countable locally compact Hausdorff case. Our proof averages arbitrary Radon probability measures along strictly positive densities to obtain quasi-invariant measures. We overcome the lack of absolute continuity of the original measure with respect to its quasi-invariant substitute by also averaging the Reiter functions along the same density.
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BibTeX
@misc{kranz2026topological,
title = {{Topological and measurewise amenability for locally compact groupoids}},
author = {Julian Kranz},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.10010},
eprint = {2611.10010},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.10010},
}
RIS
TY - UNPB
TI - Topological and measurewise amenability for locally compact groupoids
AU - Julian Kranz
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.10010
UR - https://arxiv.org/abs/2611.10010
AB - We prove the equivalence of topological and measurewise amenability for σ-compact locally compact groupoids with a Hausdorff unit space and a continuous Haar system. This in particular includes the second countable locally compact Hausdorff case. Our proof averages arbitrary Radon probability measures along strictly positive densities to obtain quasi-invariant measures. We overcome the lack of absolute continuity of the original measure with respect to its quasi-invariant substitute by also averaging the Reiter functions along the same density.
ER -