论文标题
在对称版本的Seaki定理和平坦的密度
On the symmetric version of Seaki Theorem and flat densities
论文作者
论文摘要
结果表明，对于任何$α\ in] \ frac12,1 [$都存在对称概率度量$σ$的$σ$ $σ$的hausdorff尺寸为$α$ $α$，并且$σ*σ$绝对连续连续连续使用RADON-NIKODYM衍生物。也就是说，我们获得了Seaki定理的对称版本，但是$σ*σ$的扁平radon-nikodym衍生物不能是Lipschitz函数。
It is shown that for any $α\in ]\frac12,1[$ there exists a symmetric probability measure $σ$ on the torus such that the Hausdorff dimension of the support of $σ$ is $α$ and $σ*σ$ is absolutely continuous with flat continuous Radon-Nikodym derivative. Namely, we obtain a symmetric version of Seaki Theorem but the flat Radon-Nikodym derivative of $σ*σ$ can not be a Lipschitz function.
