Abstract
We show that the strong stable foliation of the canonical extension of an Axiom A flow to an Abelian cover of a compact manifold is ergodic with respect to the product of a Gibbs measure on the manifold times the Haar measure on the fiber, as soon as it is transitive on the support of the measure. This generalizes previous results of M. Babillot, F. Ledrappier, M. Pollicott and V. Kaimanovich.
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