Geodesic
Amenability and Translation Experiments
Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 49-58

Voir la notice de l'article provenant de la source Cambridge University Press

In [11] it is shown that the deficiency of a translation experiment with respect to another on a σ-finite, amenable, locally compact group can be calculated in terms of probability measures on the group. This interesting result, brought to the writer's notice by [1], does not seem to be as wellknown in the theory of amenable groups as it should be. The present note presents a simple proof of the result, removing the σ-finiteness condition and repairing a gap in Torgersen's argument. The main novelty is the use of Wendel's multiplier theorem to replace Torgersen's approach which is based on disintegration of a bounded linear operator from L1(G) into C(G)* for G σ-finite (cf. [5], VI.8.6). The writer claims no particular competence in mathematical statistics, but hopes that the discussion of the above result from the “harmonic analysis” perspective may prove illuminating.We then investigate a similar issue for discrete semigroups. A set of transition operators, which reduce to multipliers in the group case, is introduced, and a semigroup version of Torgersen's theorem is established. 
Paterson, Alan L. T. Amenability and Translation Experiments. Canadian journal of mathematics, Tome 35 (1983) no. 1, pp. 49-58. doi: 10.4153/CJM-1983-004-6
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