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Let be a family of contractive similitudes satisfying the open set condition. Let ν be a self-similar measure associated with . We study the quantization problem for the in-homogeneous self-similar measure μ associated with a condensation system . Assuming a version of in-homogeneous open set condition for this system, we prove the existence of the quantization dimension for μ of order r ∈ (0, ∞) and determine its exact value ξr. The finiteness and positivity of the ξr-dimensional upper and lower quantization coefficient are also explored.

The quantization for in-homogeneous self-similar measures with in-homogeneous open set condition