From Jaynes' probability theory: the logic of science, I found this:
$p$ here is the joint probability distribution of $x,$ and $y$. I'm assuming the $\times$ denotes the cartesian product, but I don't really understand what this equation means, nor why it captures the assumption that $x$ and $y$ are independent.
Why does this equation capture the assumption that $x$ and $y$ are independent?