Haar measure for non-Hausdorff locally compact groups

Abstract

The paper describes two possible ways of extending the definition of Haar measure to non-Hausdorff locally compact groups. The first one forces compact sets to be measurable: with this construction, a counterexample to the existence of the Haar measure is provided. The second one makes use of closed compact sets instead of compact sets in the definition of Radon measure: this way, the classical theorems of existence and uniqueness of the Haar measure can be generalised to locally compact groups, not necessarily Hausdorff.