On a finite probability space $X \in$Set a positive measure is a function$\rho : X \to \mathbb{R}_+$ and a probability distribution is one such that $\sum_{x \in X} \rho(x) = 1$.

This space is actually a submanifold of $\mathbb{R}_{\geq 0}^{\vert X \vert}$. For $\{\frac{\partial}{\partial x^i}\}$ the canonical basis of tangent vectors on this wedge of Cartesian space, the information metric $g$ is given by