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# Wydawnictwa / Czasopisma IMPAN / Bulletin Polish Acad. Sci. Math. / Wszystkie zeszyty

## Quantization Dimension Estimate of Inhomogeneous Self-Similar Measures

### Tom 61 / 2013

Bulletin Polish Acad. Sci. Math. 61 (2013), 35-45 MSC: Primary 28A80; Secondary 60D05, 94A15. DOI: 10.4064/ba61-1-5

#### Streszczenie

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 $\mu$.

#### Autorzy

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

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