Geodesic
An $L_p$-criterion of amenability for a~locally compact group
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 186-189.

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We establish a criterion of amenability for a subgroup $H$ of a second countable locally compact topological group $G$ in terms of the left regular representation of $H$ in $L_p(G)$. 
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Ya. A. Kopylov. An $L_p$-criterion of amenability for a~locally compact group. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 2 (2005), pp. 186-189. http://geodesic.mathdoc.fr/item/SEMR_2005_2_a23/

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