Mathematical Notes

, Volume 79, Issue 5–6, pp 864–868 | Cite as

Typical ℤn-actions can be inserted only in injective ℝn-actions

  • V. V. Ryzhikov
  • S. V. Tikhonov


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 words

Lebesgue space automorphism discrete dynamical system continuous flow residual set meager set complete separable space Gδ-set 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • V. V. Ryzhikov
    • 1
  • S. V. Tikhonov
    • 2
  1. 1.M. V. Lomonosov Moscow State UniversityRussia
  2. 2.Russian State University For Trading and EconomyMoscow

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