How can I denote the set of probability distributions over a finite set? I am trying to refer to the set of probability mass functions over a finite set $A$. If the elements in the set $A$ are numbered, referring to the simplex $\Delta^{|A|-1}$ would describe exactly what I mean. Is there a similarly compact notation that I could use without assuming that the elements in $A$ are numbered? I'm trying to avoid writing the full definition, $\left\\{p:A\to[0,1]\middle\vert \sum_{a\in A} p(a)=1\right\\}$ because that would slow down the flow of the paragraph considerably.

I think compact notation slows down flow more than do more words. Why not just say "the set of probability distributions on $A$"? If necessary, precede that by saying a probability distribution is a nonnegative real valued function on $A$ that sums to $1$.