论文标题
$ \ mathbb {r}^n $中分形集的一个限制投影问题
A restricted projection problem for fractal sets in $\mathbb{R}^n$
论文作者
论文摘要
令$γ：[-1，1] \ to \ mathbb {r}^n $为平滑的曲线，是非分级的。以$ m \ le n $和borel set $ e \ subset [0，1]^n $。我们证明，$ e $对$ m $ e $的正交预测在[-1，1] $ in [-1，1] $ in [-1，1] $ in [-1，1] $ in [-1，1] $中的$γ$的正交预测几乎每个$θ\ in [-1，1] $具有hausdorff dimension $ \ min \ min \ min \ min \ min \ min \ min \ min \ dim（e）$。
Let $γ: [-1, 1]\to \mathbb{R}^n$ be a smooth curve that is non-degenerate. Take $m\le n$ and a Borel set $E\subset [0, 1]^n$. We prove that the orthogonal projection of $E$ to the $m$-th order tangent space of $γ$ at $θ\in [-1, 1]$ has Hausdorff dimension $\min\{m, \dim(E)\}$ for almost every $θ\in [-1, 1]$.
