A disintegration theorem for non-second-countable etale groupoids

We give a self-contained account of a version of Renault’s disintegration theorem for (twisted) C${}^{\ast }$-algebras of not necessarily Hausdorff étale groupoids that can be covered by countably many open bisections. As an application we discuss the $I$-norm, crossed product decompositions by inverse semigroup actions, and KMS-states and weights for general étale groupoid C${}^{\ast }$-algebras.