可数分支系统的极大化Bernoulli测度和维数间隙
Maximising Bernoulli measures and dimension gaps for countable branched systems
摘要：
Kifer，Peres和Weiss证明了存在$c_0>0,$使得对于任何概率测度$μ$，$\dim μ\leq 1-c_0$使得连分数展开式的位数i.i.d.随机变量。本文证明了在这类测度中，存在一个维数最大的测度。我们的结果也适用于更一般的设置可数分支系统。
英文摘要：
Kifer, Peres, and Weiss proved that there exists $c_0>0,$ such that $\dim μ\leq 1-c_0$ for any probability measure $μ$ which makes the digits of the continued fraction expansion i.i.d. random variables. In this paper we prove that amongst this class of measures, there exists one whose dimension is maximal. Our results also apply in the more general setting of countable branched systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
