Lower quantization coefficient and the $F$-conformal measure
Volume 122 / 2011
Colloquium Mathematicum 122 (2011), 255-263
MSC: 60Exx, 28A80, 94A34.
DOI: 10.4064/cm122-2-11
Abstract
Let $F=\{ f^{(i)} : 1\leq i\leq N\}$ be a family of Hölder continuous functions and let $\{\varphi_i : 1 \leq i\leq N\}$ be a conformal iterated function system. Lindsay and Mauldin's paper [Nonlinearity 15 (2002)] left an open question whether the lower quantization coefficient for the $F$-conformal measure on a conformal iterated funcion system satisfying the open set condition is positive. This question was positively answered by Zhu. The goal of this paper is to present a different proof of this result.
