# Absolute continuity of Bernoulli convolutions for algebraic parameters

@article{Varju2016AbsoluteCO,
title={Absolute continuity of Bernoulli convolutions for algebraic parameters},
author={P'eter P'al Varj'u},
journal={Journal of the American Mathematical Society},
year={2016}
}
• P. P. Varj'u
• Published 31 January 2016
• Computer Science
• Journal of the American Mathematical Society
<p>We prove that Bernoulli convolutions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="mu Subscript lamda"> <mml:semantics> <mml:msub> <mml:mi>μ<!-- μ --></mml:mi> <mml:mi>λ<!-- λ --></mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">\mu _\lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are absolutely continuous provided the parameter <inline-formula content-type…
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The Bernoulli convolution with parameter $\lambda\in(0,1)$ is the probability measure $\mu_\lambda$ that is the law of the random variable $\sum_{n\ge0}\pm\lambda^n$, where the signs are independent
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