Rigidity and cocycles for ergodic actions of semi-simple Lie groups
Harry Furstenberg (1979-1980)
Séminaire Bourbaki
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Rigidity and cocycles for ergodic actions of semi-simple Lie groups
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Let G be a group of homeomorphisms of a nondiscrete, locally compact, σ-compact topological space X and suppose that a Haar measure on X exists: a regular Borel measure μ, positive on nonempty open sets, finite on compact sets and invariant under the homeomorphisms from G. Under some mild assumptions on G and X we prove that the measure completion of μ is the unique, up to a constant factor, nonzero, σ-finite, G-invariant measure defined on its domain iff μ is ergodic and the G-orbits...