TL;DR
This paper investigates conditions under which a locally compact groupoid admits a Haar system, showing that not all do, but providing a construction method when certain subgroupoids have Haar systems.
Contribution
It demonstrates that a Haar system does not always exist for groupoids with open range maps and offers a construction method using subgroupoids that do admit Haar systems.
Findings
Not all locally compact groupoids with open range maps admit Haar systems.
A Haar system can be constructed if both the stability groupoid and the quotient admit Haar systems.
Abstract
It is shown that a locally compact groupoid with open range map does not always admit a Haar system. It then is shown how to construct a Haar system if the stability groupoid and the quotient by the stability groupoid both admit one.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Topics in Algebra · Advanced Banach Space Theory