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Computing probability of Borelian languages Arfi

The Kolmogorov extension theorem shows that, for any probability law π on A∗, there exists one and only one probability measure, namely Pπ, on the family of Borelian languages of Aω such that Pπ(wA) = π(w). We give in this paper a method to compute the probability mesure, given by the Kolmogorov extension theorem, of Borelian languages of infinite words on a finite alphabet A. This method becomes effective in the case of rational Borelian languages when the probability law is computable, as in the case of probability law defined by an automaton.