Marc Kessebohmer

Geometric mean quantization via adaptive approximation

Let $\nu$ be a compactly supported Borel probability measure on $\mathbb R^{d}$ with $\nu(B(x,r))\leq Cr^{a}$ for some $a>0$. Refine a dyadic cube exactly when its mass is at least $t$, and let $\mathcal{L}_{\nu}(t)$ be the mean depth at which this refinement stops. We show that the lower and upper geometric-mean quant...