Property (T) and actions on infinite measure spaces

The aim of the article is to provide a characterization of Kazhdan’s property (T) for locally compact, second countable pairs of groups $H\subset G$ in terms of actions on infinite, $\sigma$-finite measure spaces. It is inspired by the recent characterization of the Haagerup property by similar actions due to T. Delabie, A. Zumbrunnen and the author.