on uniformly amenable groups - American Mathematical Society
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on uniformly amenable groups - American Mathematical Society
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL Volume
102, Number
4, April
SOCIETY 1988
ON UNIFORMLY AMENABLE GROUPS JANUSZ WYSOCZÁNSKI ABSTRACT. We consider the conditions of the uniform amenability of discrete groups. The equivalence of the uniform Folner and Kesten conditions is proved. Also an example of the group which is amenable but not uniformly amenable is given.
1. Introduction. There are many well-known characterizations of amenable groups. We consider in this paper two of them given by E. F0lner [2] and H. Kesten [9]. The relationships between these conditions of amenability were considered by V. A. Kaimanovich and V. M. Vershik [6] in the context of random walks on groups. Some properties related to amenability for discrete groups were introduced by M. Bozejko [1] and G. Keller [7]. They called the discrete amenable group G uniformly amenable if there exists a function a: (0,1) x N —*N such that for every finite subset A of the group G and every e G (0,1) there is a finite subset U of G
