Asymptotic local uniformity of the quantization error for Ahlfors-David probability measures

Sanguo Zhu

Let $\mu$ be an Ahlfors-David probability measure on ${\mathbb{R}}^q$, namely, there exist some constants $s_0>0$ and ${\epsilon }_0,C_1,C_2>0$ such that \[ C_1ε^{s_0}\leqμ(B(x,ε))\leq C_2ε^{s_0…