论文标题
均匀组的单位Hausdorff密度的集合
On sets with unit Hausdorff density in homogeneous groups
论文作者
论文摘要
这是一个长期以来的猜想，如果$ e $具有有限的hausdorff尺寸，则在尺寸$α\ ge 0 $和$ \ mathscr {h}^α\ llcorner e $几乎在任何地方都具有单位密度，那么$ e $是$α$ - $ - 可调整的设置。我们在假设环境公制空间是具有平滑盒标准的同质组的假设下证明了这一猜想。
It is a longstanding conjecture that given a subset $E$ of a metric space, if $E$ has finite Hausdorff measure in dimension $α\ge 0$ and $\mathscr{H}^α\llcorner E$ has unit density almost everywhere, then $E$ is an $α$-rectifiable set. We prove this conjecture under the assumption that the ambient metric space is a homogeneous group with a smooth-box norm.
