Ergodicity of Cocycles. 1: General Theory
نویسنده
چکیده
We prove severaìautomatic' ergodicity results for cocycles on a discrete nonsingular ergodic equivalence relation on a probability space (X; S;) with values in virtually nilpotent groups. The hypotheses required for automatic ergodicity are invari-ance or quasi-invariance of the cocycles under asymptotically central automorphisms of the equivalence relation. If the cocycles have certain recurrence properties then the condition of virtual nilpotency can be relaxed. In a subsequent paper these ideas will be applied to ergodicity of noncompact and nonabelian covers of horocycle foliations on compact manifoldswith nonconstant negative curvature.
منابع مشابه
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