关于整自仿射集的勒贝格测度
On Lebesgue measure of integral self-affine sets
摘要：
设$A$是一个扩展整数$n\times n$矩阵，$D$是$Z^n$的有限子集.自仿射集$T=T(A,D)$是满足等式$A(T)=\cup_{d\in D} (T+d)$的唯一紧集.给出了计算自仿射集$T$的勒贝格测度、$u\in Z^n$的交测度$T\cap (T+u)$以及自仿射集$T(A,D_1)\cap T(A,D_2)$与不同集$D_1,D_2\subset Z^n$的交测度的有效算法.
英文摘要：
Let $A$ be an expanding integer $n\times n$ matrix and $D$ be a finite subset of $Z^n$. The self-affine set $T=T(A,D)$ is the unique compact set satisfying the equality $A(T)=\cup_{d\in D} (T+d)$. We present an effective algorithm to compute the Lebesgue measure of the self-affine set $T$, the measure of intersection $T\cap (T+u)$ for $u\in Z^n$, and the measure of intersection of self-affine sets $T(A,D_1)\cap T(A,D_2)$ for different sets $D_1,D_2\subset Z^n$.
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