Let G be a locally compact group. Then G is known to be amenable if and only if it has Reiter’s property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα−mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x). We give a formulation of property (P1) that extends naturally to locally compact quantum groups i...

We study the concept of α-amenability of commutative hypergroups K. We establish several characterizations of α-amenability by combining results of [1] and [2] and adding the Glicksberg-Reiter property. In addition, as examples compact K and discrete polynomial hypergroups on N0 are discussed. 2000 Mathematics Subject Classification: Primary 43A62, Secondary 46H25

In this paper we propose a formalization of probable innocence, a notion of probabilistic anonymity that is associated to “realistic” protocols such as Crowds. We analyze critically two different definitions of probable innocence from the literature. The first one, corresponding to the property that Reiter and Rubin have proved for Crowds, aims at limiting the probability of detection. The seco...

Interest in the Reiter strain of Treponema pallidum, a nonpathogenic, cultivatable, anaerobic spirochete, has been stimulated by the demonstration that the organism possesses four antigens; one, a thermolabile protein, being group specific for treponemes (D'Alessandro et al., 1949). This antigen has recently been employed in a Reiter protein complement fixation test for syphilis (Cannefax and G...