K-flots et théorème de renouvellement

It is shown that for certain dynamical systems (among them Bernoulli systems, some Markov chains and quasi-Bernoulli systems), and for a certain class of functions, either the flow built under the function is K, or the set of values of the function is arithmetical. From that result one deduces a generalization of the classical renewal theorem, with a necessary and sufficient condition.