Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 35-45
MSC: Primary 28A80; Secondary 60D05, 94A15.
DOI: 10.4064/ba61-1-5
Abstract
We consider an inhomogeneous measure $\mu $ with the inhomogeneous part a self-similar measure $\nu $, and show that for a given $r\in (0,\infty )$ the lower and the upper quantization dimensions of order $r$ of $\mu $ are bounded below by the quantization dimension $D_r(\nu )$ of $\nu $ and bounded above by a unique number $\kappa _r\in (0, \infty )$, related to the temperature function of the thermodynamic formalism that arises in the multifractal analysis of $\mu $.
