On the dimension of Bernoulli convolutions for all transcendental parameters

• 成果类型: Article
• 署名作者: Varju, Peter P.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2019.189.3.9
• 发表日期: 2019
• 页码: 1001-1011
• 关键词: self-similar sets; Absolute continuity; FAMILY

摘要

The Bernoulli convolution nu(lambda) with parameter lambda is an element of (0, 1) is the probability measure supported on R that is the law of the random variable Sigma +/-lambda(n), where the +/- are independent fair coin-tosses. We prove that dim nu(lambda) = 1 for all transcendental lambda is an element of (1/2, 1).