Ergodic-theoretic Properties of Certain Bernoulli Convolutions
نویسنده
چکیده
In [17] the author and A. Vershik have shown that for β = 1 2 (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 β-shift, and the natural extension of the β-shift provided with the measure equivalent to the Erdös measure, is Bernoulli. In this note we extend this result to all Pisot parameters β (modulo some general arithmetic conjecture) and an arbitrary “sufficient” alphabet.
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