Juschenko, KateMonod, Nicolas2012-07-032012-07-032012-07-03201310.4007/annals.2013.178.2.7https://infoscience.epfl.ch/handle/20.500.14299/83352WOS:000320582400007We provide the first examples of finitely generated simple groups that are amenable (and infinite). This follows from a general existence result on invariant states for piecewise-translations of the integers. The states are obtained by constructing a suitable family of densities on the classical Bernoulli space.text::journal::journal article::research article