"I suggest making it explici..."


by Nate Soares Mar 3 2016 updated Mar 3 2016

I suggest making it explicit that $~$P$~$ is a distribution over a (possibly infinite) set of variables (or propositions naming symbols, or whatever your preferred formalization is), and that $~$P(x)$~$ is shorthand for $~$P(X=x)$~$ when $~$X$~$ is unambiguous. This is one of those things that I had to figure out myself, which had confused me historically in my youth, and led me to think that all the $~$P$~$ notation was probably informal argument rather than formal math.