To make this all work smoothly, let's situate the stochastic states inside of a containing vector space.

Let D be the definite states -- these are the nodes in the transition graph.

The vector space that we will work within is the space of real-valued functions on D, i.e. \\(\mathbb{R}^D\\).

Let \\(\Delta \subset R^D\\) be the simplex in F, meaning the functions taking values in [0,1] where all the values sum to 1.

\\(\Delta\\) is all the probability distributions over D, all the stochastic states.

Let D be the definite states -- these are the nodes in the transition graph.

The vector space that we will work within is the space of real-valued functions on D, i.e. \\(\mathbb{R}^D\\).

Let \\(\Delta \subset R^D\\) be the simplex in F, meaning the functions taking values in [0,1] where all the values sum to 1.

\\(\Delta\\) is all the probability distributions over D, all the stochastic states.