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This is mainly an expository text on the Haagerup property for countablegroupoids equipped with a quasi-invariant measure, aiming to complete anarticle of Jolissaint devoted to the study of this property for probabilitymeasure preserving countable equivalence relations. We show that our definitionis equivalent to the one given by Ueda in terms of the associated inclusion ofvon Neumann algebras. It makes obvious the fact that treeability implies theHaagerup property for such groupoids. For the sake of completeness, we alsodescribe, or recall, the connections with amenability and Kazhdan property (T).

Old and new about treeability and the Haagerup property for measured groupoids