Weighted approach to general entropy function

The definition of weighted entropy allows to calculate the entropy of the mixture of measures. In this paper, we investigate the problem of equivalent definition of the general entropy function in the weighted form. We show that under a reasonable condition, which is satisfied by the well-known Shannon, Rényi and Tsallis entropies, every entropy function can be defined equivalently in the weighted way. As a corollary, we show how to use the weighted form to compute Tsallis entropy of the mixture of measures.