Abstract
In this paper using the Banach limit we have determined a Gibbs-like measure μh supported by a cookie-cutter set E which is generated by a single cookie-cutter mapping f. For such a measure μh and r∈(0,+∞) we have shown that there exists a unique κr∈(0,+∞) such that κr is the quantization dimension function of the probability measure μh, and we established its functional relationship with the temperature function of the thermodynamic formalism. The temperature function is commonly used to perform the multifractal analysis, in our context of the measure μh. In addition, we have proved that the κr-dimensional lower quantization coefficient of order r of the probability measure is positive.
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