Abstract
Consider en =i n f e xplogx−f(x) � dP(x), where p is a probability measure on IR d and the infimum is taken over all measurable maps f:IR d →IR d with |f(IR d )| � n. We study solutions f of this minimization problem. For absolutely continuous distri- butions and for self-similar distributions we derive the exact rates of convergence to zero of the nth quantization error en as n →∞ . We establish a relationship between the quantization dimension that rules the rates and the Hausdorff dimension of P.
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