Theorems on the variable-length intrinsic randomness

In this paper we address variable-length intrinsic randomness problems (in the sense of Vembu and Verdu) for countably infinite source alphabet X under the (unnormalized) divergence distance, the normalized conditional divergence distance, and the variational distance. It turns out that under all three kinds of approximation measures the variable-length intrinsic randomness still takes the same value, called the inf-entropy rate of the source.