A Generalization of Renault's Theorem for Cartan Subalgebras

Abstract

We prove a generalized version of Renault's theorem for Cartan subalgebras. We show that the original assumptions of second countability and separability are not needed. This weakens the assumption of topological principality of the underlying groupoid to effectiveness.

10 pages, added references, simplified proof for Prop. 3.3, updated author contact info, fixed typos. Accepted for publication in Proc. Amer. Math. Soc