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Let G be a σ-compact locally compact group and H a closed subgroup. We characterize the lack of Kazhdan's property T for the pair (G, H) by the genericity of G-actions on the hyperfinite II1 factor with a certain asymptotic Abelianness property relative to H, as well as by the genericity of measure-preserving G-actions on a nonatomic standard probability space that are weakly mixing for H. The latter furnishes a definitive generalization of a classical theorem of Halmos for single automorphismsdoi:10.1515/crelle.2008.077 fatcat:5h4bwrm3r5cj5gncnkjcemauay