Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques

Abstract

AbstractWe call nilmanifold every compact space X on which a connected locally compact nilpotent group acts transitively. We show that, if X is a nilmanifold and f is a continuous function on X, then, for all x in X and a in N, the sequenceconverges. We give a process for the computation of the limit. A similar result for the continuous means is presented.