关于测度和无穷伯努利卷积的一个注记(英文)

A Note on Measure and Infinite Bernoulli Convolutions

设a :={ai} ∞i=1是正实数序列 ,μa 是支撑在Sμa 上的无穷伯努利卷积 ,本文给出了Sμa 的Hausdorff维数和Hausdorff测度 ,它改进了CooperMJP的相应结果 .

Let a:={a i} ∞ i=1 be a sequence of positive real numbers and a be the infinite Bernoulli convolution with support denoted by S μ a and defined by the sequence. In this paper, the Hausdorff dimension and measure of S μ a are given , which improve M J P Cooper′s result.