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- For a lattice GGG0, the induced GGG1-action on GGG2 is not common for GGG3 in general, nevertheless it stays a canonical boundary and in Furstenberg’s authentic work serves as the Poisson boundary for sure random walks (Bassi et al., 2021).
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- For a minimal compact ∂FG\partial_F G∂FG11-space ∂FG\partial_F G∂FG12, a ∂FG\partial_F G∂FG13-boundary is a minimal strongly proximal extension ∂FG\partial_F G∂FG14, and the universal object ∂FG\partial_F G∂FG15 specializes to the classical Furstenberg boundary when ∂FG\partial_F G∂FG16 is a point (Naghavi, 2019).
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