The equivalence of some bernoulli convolutions to lebesgue measure

R. Daniel Mauldin, K. Simon

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

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].

Original languageEnglish
Pages (from-to)2733-2736
Number of pages4
JournalProceedings of the American Mathematical Society
Volume126
Issue number9
Publication statusPublished - 1998

Fingerprint

Bernoulli Convolution
Lebesgue Measure
Convolution
Equivalence
Absolutely Continuous
Series

Keywords

  • Bernoulli convolution
  • Equivalent measures

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 126, No. 9, 1998, p. 2733-2736.

Research output: Contribution to journalArticle

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