Pi notation under a sigma

Question

I came across a bunch of notations under a sigma, but I can't understand what They all mean.

$\sum_{f\in \prod_{a\in A}B_a}$

$A$ and $B_a$ are sets, but the whole thing is hard to figure out.

I came across that here

edit:

full expression $\sum_{f\in \prod_{a\in A}B_a}\quad \prod_{a\in A}{h(a,f(a))}$

Answer 1

$$\sum_{f \in \prod_{a \in A} B_a}\; \prod_{a \in A} h(a,f(a))$$ is the sum of products of $h(a,f(a))$ for all $f$ in the cartesian product of the $B_a$'s. Thus if $A = \{1, 2, 3\}$ you have three sets $B_1$, $B_2$, $B_3$, and you add $h(1, f(1)) h(2, f(2)) h(3,f(3))$ over all choices of $(f(1), f(2), f(3))$ where $f(1)$ is a member of $B_1$, $f(2)$ is a member of $B_2$, and $f(3)$ is a member of $B_3$.