Lower quantization coefficient and the $F$-conformal measure

Volume 122 / 2011

Mrinal Kanti Roychowdhury Colloquium Mathematicum 122 (2011), 255-263 MSC: 60Exx, 28A80, 94A34. DOI: 10.4064/cm122-2-11


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.


  • Mrinal Kanti RoychowdhuryDepartment of Mathematics
    The University of Texas-Pan American
    1201 West University Drive
    Edinburg, TX 78539-2999, U.S.A.

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