The Choquet-Deny theorem and distal properties of totally disconnected locally compact groups of polynomial growth.
On heredity of strongly proximal actions
We prove that action of a semigroup on compact metric space by continuous selfmaps is strongly proximal if and only if action on is strongly proximal. As a consequence we prove that affine actions on certain compact convex subsets of finite-dimensional vector spaces are strongly proximal if and only if the action is proximal.
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