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Let $\mu$ be a Borel probability measure associated with an iterated functionsystem consisting of a countably infinite number of contracting similaritiesand an infinite probability vector. In this paper, we study the quantizationdimension of the measure $\mu$ with respect to the geometric mean error. Thequantization for infinite systems is different from the well-known finite caseinvestigated by Graf and Luschgy. That is, many tools which are used in thefinite setting, for example, existence of finite maximal antichains, fail inthe infinite case. We prove that the quantization dimension of the measure$\mu$ is equal to its Hausdorff dimension which extends a well-known result ofGraf and Luschgy for the finite case to an infinite setting. In the lastsection, we discuss the stability of quantization dimension for infinitesystems.

Quantization dimension and stability for infinite self-similar measures with respect to geometric mean error