Abstract
Given a measure μ on the circle, we study the relations between the entropy of the multiplication by an integerp and the conservativity for the translations by thep-acid rational numbers. We get a criterium for μ-almost every point to be normal in a basisq prime top, and generalizations of the result of D. Rudolph about measures which are invariant by multiplication byp andq.
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Ce travail a été terminé pendant le séjour de l'auteur au Japon à l'invitation de la Japan Society for the Promotion of Sciences.
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Host, B. Nombres normaux, entropie, translations. Israel J. Math. 91, 419–428 (1995). https://doi.org/10.1007/BF02761660
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DOI: https://doi.org/10.1007/BF02761660