Probability Simplex

Let $l$ be a natural number with $l\ge 1$, and let $\mathbb{R}^l$ denote Euclidean space. The probability simplex $\Delta^l$ is the set

Elements of $\Delta^l$ are called probability vectors. For $\sigma\in\{1,\dots,l\}$ we write $\delta_\sigma$ for the $\sigma$-th standard basis vector of $\mathbb{R}^l$, which is an element of $\Delta^l$.