2002/03/06 by Nikita Sidorov, Sidorov, Nikita
Mathematics · #11R06 #28D05 #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Dynamics and Fractals #Mathematical and Theoretical Analysis #Number Theory (math.NT) #math.DS #math.NT #msc:11R06 #msc:28D05
paper · pdf · doi:10.48550/arxiv.math/0203056
10 pages, Latex2e
arxiv created 2002/03/06 · openalex publication_date 2002/03/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [17] the author and A. Vershik have shown that for \be=\frac12(1+√5) and the alphabet \0,1\ the infinite Bernoulli convolution (= the Erdös measure) has a property similar to the Lebesgue measure. Namely, it is quasi-invariant of type II1 under the \be-shift, and the natural extension of the \be-shift provided with the measure equivalent to the Erdös measure, is Bernoulli. In this note we extend this result to all Pisot parameters \be (modulo some general arithmetic conjecture) and an arbitrary "sufficient" alphabet.