论文标题
在与双倍图相关的单数连续措施上
On a family of singular continuous measures related to the doubling map
论文作者
论文摘要
在这里，我们研究了一些可以用1个周期功能的无限Riesz产品表示的措施，并且与倍增图有关。我们表明，相对于Lebesgue度量，这些措施纯粹是奇异的连续性，并且它们的分布函数满足了原点附近的超多种物质渐近差异，因此提供了一个极端的奇异措施典例，包括Thue-Morse Mesure。
Here, we study some measures that can be represented by infinite Riesz products of 1-periodic functions and are related to the doubling map. We show that these measures are purely singular continuous with respect to Lebesgue measure and that their distribution functions satisfy super-polynomial asymptotics near the origin, thus providing a family of extremal examples of singular measures, including the Thue--Morse measure.
