论文标题
Furstenberg集群猜想和曼德布罗特渗透
Furstenberg sumset conjecture and Mandelbrot percolations
论文作者
论文摘要
在本文中，我们将Hochman和Shmerkin的投影定理扩展到作用于通过一维迭代功能系统的典型映射进行的千古量测量的Mandelbrot Cascades的产品度量，而没有任何分离条件。因此，我们将furstenberg集合定理扩展到符号空间上的子缩影图像，并将其延伸到不变集上的mandelbrot渗透。我们还获得了伯努利卷积和曼德布罗级级联措施的卷积的尺寸结果。
In this paper we extend Hochman and Shmerkin's projection theorem to product measures of Mandelbrot cascades acting on ergodic measures imaged through canonical mappings of one-dimensional iterated function systems without any separation conditions. Consequently we extend Furstenberg sumset theorem to images of subshifts on symbolic spaces, and to Mandelbrot percolations on invariant sets. We also obtain dimension results for convolutions of Bernoulli convolutions and that of Mandelbrot cascade measures.
