Abstract
AbstractLet p and q be relatively prime natural numbers. Define T0 and S0 to be multiplication by p and q (mod 1) respectively, endomorphisms of [0,1).Let μ be a borel measure invariant for both T0 and S0 and ergodic for the semigroup they generate. We show that if μ is not Lebesgue measure, then with respect to μ both T0 and S0 have entropy zero. Equivalently, both T0 and S0 are μ-almost surely invertible.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Cited by
91 articles.
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