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A dimension formula for Bernoulli convolutions

✍ Scribed by François Ledrappier; Anna Porzio

Publisher
Springer
Year
1994
Tongue
English
Weight
689 KB
Volume
76
Category
Article
ISSN
0022-4715

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📜 SIMILAR VOLUMES

Dimension of a Family of Singular Bernou
Dimension of a Family of Singular Bernoulli Convolutions
✍ K.S. Lau 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 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. Erdös-Salem proved

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Following Crapo [2], let `(x, y)(M)=x r(M) y r(M\*) , where K=Z[x, y]. Lemma 1. `(x, y) &1 =`(&x, &y).

Explicit formulas for degenerate Bernoul
Explicit formulas for degenerate Bernoulli numbers
✍ F.T. Howard 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 380 KB

The 'degenerate' Bernoulli numbers tim(2) can be defined by means of the exponential generating function x((1 + 2x) 1/~ -1)-1. L. Carlitz proved an analogue of the Staudt-Clausen theorem for these numbers, and he showed that/3m(2) is a polynomial in 2 of degree ~< m. In this paper we find explicit f