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On the Smoothness Properties of a Family of Bernoulli Convolutions

✍ Scribed by Erdos, Paul


Book ID
125465156
Publisher
John Hopkins University Press
Year
1940
Tongue
English
Weight
552 KB
Volume
62
Category
Article
ISSN
0002-9327

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Dimension of a Family of Singular Bernou
✍ K.S. Lau πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 705 KB

Let \(\left\{X_{n}\right\}_{n=0}^{\infty}\) be a sequence of i.i.d. Bernoulli random variables (i.e., \(X_{n}\) takes values \(\{0,1\}\) with probability \(\frac{1}{2}\) each), let \(X=\sum_{n=0}^{\infty} \rho^{n} X_{n}\), and let \(\mu\) be the corresponding probability measure. ErdΓΆs-Salem proved