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Let G be a countable discrete group that act minimally on a compact Hausdorff space X by homeomorphisms. Our goal is to establish the equivalence between the faithfulness of the action of G on the generalized Furstenberg boundary F (G, X) and a weakened version of the generalized Powers' averaging property. This result provides valuable insights into the state space of the crossed product C (X) ₑG.
Behrouzi et al. (Sat,) studied this question.
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