Some remarks on output measures

An output measure is an image of a uniform Bernoulli measure on finitely many states. We discuss “generalized Bernoulli” measures of Freiling and Jackson in [Real Analysis Exchange, Summer Symposium, Lexington, 2002, pp. 11-34], and answer several questions posed in that paper, in particular we establish a condition when such a measure is a finitary output measure. Answering D. Goldstein's question, we characterize output measures via block codes in terms of walks on labeled graphs with special adjacency matrices.