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Shannon's classical information theory uses probability theory to analyzechannels as mechanisms for information flow. In this paper, we generalizeresults of Martin, Allwein and Moskowitz for binary channels to show how somemore modern tools - probabilistic monads and domain theory in particular - canbe used to model classical channels. As initiated Martin, et al., the point ofdeparture is to consider the family of channels with fixed inputs and outputs,rather than trying to analyze channels one at a time. The results show thatdomain theory has a role to play in the capacity of channels; in particular,the (n x n)-stochastic matrices, which are the classical channels having thesame sized input as output, admit a quotient compact ordered space which is adomain, and the capacity map factors through this quotient via aScott-continuous map that measures the quotient domain. We also comment on howsome of our results relate to recent discoveries about quantum channels andfree affine monoids.

Probabilistic Monads, Domains and Classical Information