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

Goun2
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    $\prod_{a\in A} B_a$ might denote the set product (Cartesian product) of the $B_a$’s. For example, $\prod_{x\in {0,1}} B_x$ is the set $B_0\times B_1$. – user722227 Jun 30 '20 at 00:30
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    Including the article/book where you found them into the question may be helpful for others to see what's going on and thus explain. Thanks. – Alexey Burdin Jun 30 '20 at 00:30
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    Usually there would be something after this, say $\sum_{f \in \prod_{a \in A} B_a} c(f)$, which would mean the sum of $c(f)$ over all $f$ in the Cartesian product of the $B_a$'s. – Robert Israel Jun 30 '20 at 00:34
  • I added a link to the topic where I found it, thanks. – Goun2 Jun 30 '20 at 01:00
  • @RobertIsrael could you please translate this ? $\sum_{f\in \prod_{a\in A}B_a}\quad \prod_{a\in A}{h(a,f(a))}$ – Goun2 Jun 30 '20 at 01:45

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$$\sum_{f \in \prod_{a \in A} B_a}\; \prod_{a \in A} h(a,f(a))$$ 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 $B_3$.

Robert Israel
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