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Siberian Mathematical Journal

, Volume 59, Issue 6, pp 1094–1099 | Cite as

The Rao–Reiter Criterion for the Amenability of Homogeneous Spaces

  • Ya. A. KopylovEmail author
Article
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Abstract

We prove that a homogeneous space G/H, with G a locally compact group and H a closed subgroup of G, is amenable in the sense of Eymard–Greenleaf if and only if the quasiregular action πΦ of G on the unit sphere of the Orlicz space LΦ(G/H) for some N-function Φ ∈ Δ2 satisfies the Rao–Reiter condition (PΦ).

Keywords

locally compact group homogeneous space amenability N-function Orlicz space Δ2-condition 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

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