Rényi entropy dimension of the mixture of measures

Rényi entropy dimension describes the rate of growth of coding cost in the process of lossy data compression in the case of exponential dependence between the code length and the cost of coding. In this paper we generalize the Csiszár estimation of the Rényi entropy dimension of the mixture of measures for the case of general probability metric space. This result determines the cost of encoding of the information which comes from the combined sources assuming its exponential growth. Our proof relies on an equivalent definition of the Rényi entropy in weighted form which allows to deal well with a calculation of the entropy of the mixture of measures.