On the Absolute Continuity of the Blackwell Measure

In 1957, Blackwell expressed the entropy of hidden Markov chains using a measure which can be characterised as an invariant measure for an iterated function system with place-dependent weights. This measure, called the Blackwell measure, plays a central role in understanding the entropy rate and other important characteristics of fundamental models in information theory. We show that for a suitable set of parameter values the Blackwell measure is absolutely continuous for almost every parameter in the case of binary symmetric channels.