Absolute continuity of Bernoulli convolutions, a simple proof (Q1920888)
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scientific article; zbMATH DE number 913761
| Language | Label | Description | Also known as |
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| English | Absolute continuity of Bernoulli convolutions, a simple proof |
scientific article; zbMATH DE number 913761 |
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Absolute continuity of Bernoulli convolutions, a simple proof (English)
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6 July 1997
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The authors give a new simplified proof that the infinite Bernoulli convolution \(\nu_\lambda\) of the measures \[ \textstyle{{1\over 2}} (\delta_{-\lambda^n}+\delta_{\lambda^n}) \] for \(n\in\mathbb{N}\) and \({1\over 2}<\lambda<1\) is absolutely continuous with \(L^2\)-density. The proof is based on differentiation techniques for measures.
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differentiation of measures
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infinite Bernoulli convolution
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\(L^ 2\)-density
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