2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68330We extend the Delorme-Guichardet characterization of Kazhdan property $T$ groups to $r$-discrete measured groupoids. We give several applications, in particular to stability results of Kazhdan property $T$ and to the study of cocycles taking values in a group having the Haagerup property.43 pagesDynamical SystemsOperator Algebras22F10; 22D40; 28D15; 28D99; 37A15; 37A20text