Typical ℤn-actions can be inserted only in injective ℝn-actions
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We study actions of the groups ℤn and ℝn by Lebesgue space automorphisms. We prove that a typical ℤn-action can be inserted only in injective actions of ℝn, n ∈ ℕ. We give a simple proof of the fact that a typical ℤ2-action cannot be inserted in an ℝ-action.
Key wordsLebesgue space automorphism discrete dynamical system continuous flow residual set meager set complete separable space Gδ-set
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