Convergence of differential entropies

Calculation of the differential entropy of the limiting density of a sequence of probability density functions (pdf) is an interesting mathematical problem and is important in asymptotic analysis of communication systems. In such cases, it would be of interest to know if the limit of the differential entropies H_n, corresponding to the sequence of pdf f_n, is equal to the differential entropy H, of the limiting pdf f. In this correspondence, we establish sufficient conditions under which H_n → H.