### Abstract

Since the 1930's many authors have studied the distribution v\ of the random series Y_{λ} = ∑ ±λ^{n} where the signs are chosen independently with probability (1/2,1/2) and 0 <A <1. Solomyak recently proved that for almost every λ ∈ [1/2, 1], the distribution ν_{λ} is absolutely continuous with respect to Lebesgue measure. In this paper we prove that ν_{λ} is even equivalent to Lebesgue measure for almost all λ ∈ [1/2, 1].

Original language | English |
---|---|

Pages (from-to) | 2733-2736 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 126 |

Issue number | 9 |

Publication status | Published - 1998 |

### Fingerprint

### Keywords

- Bernoulli convolution
- Equivalent measures

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*126*(9), 2733-2736.

**The equivalence of some bernoulli convolutions to lebesgue measure.** / Daniel Mauldin, R.; Simon, K.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 126, no. 9, pp. 2733-2736.

}

TY - JOUR

T1 - The equivalence of some bernoulli convolutions to lebesgue measure

AU - Daniel Mauldin, R.

AU - Simon, K.

PY - 1998

Y1 - 1998

N2 - Since the 1930's many authors have studied the distribution v\ of the random series Yλ = ∑ ±λn where the signs are chosen independently with probability (1/2,1/2) and 0 <A <1. Solomyak recently proved that for almost every λ ∈ [1/2, 1], the distribution νλ is absolutely continuous with respect to Lebesgue measure. In this paper we prove that νλ is even equivalent to Lebesgue measure for almost all λ ∈ [1/2, 1].

AB - Since the 1930's many authors have studied the distribution v\ of the random series Yλ = ∑ ±λn where the signs are chosen independently with probability (1/2,1/2) and 0 <A <1. Solomyak recently proved that for almost every λ ∈ [1/2, 1], the distribution νλ is absolutely continuous with respect to Lebesgue measure. In this paper we prove that νλ is even equivalent to Lebesgue measure for almost all λ ∈ [1/2, 1].

KW - Bernoulli convolution

KW - Equivalent measures

UR - http://www.scopus.com/inward/record.url?scp=22044454340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22044454340&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:22044454340

VL - 126

SP - 2733

EP - 2736

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 9

ER -