Abstract: In this paper, a class of small-devitions theorems for the relative entropy densities of the sequence of arbitrary random variables are discussed by comparing between the sequence of arbitrary distributions and the seqence of independent distributions. As corollaries, some Shannon-Mcmillan theorems are obtained and some results for the discrete information source which has been obtained by authors before are extended.

Key words: Shannon-Mcmillan theorem, small-deviations theorem, relative entropy density, discrete information source