Is this a summatory multiplication?

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I'm learning probability and I've just found this on a book:

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The bold $x$ is $x=(x_1,x_2,...,x_n)$.

I'm not sure what this means. I think I have to multiply all of the sums of each element of the bold $x$, like this:

$$\sum_xP(x)=\sum_{x_1}P(x_1)·\sum_{x_2}P(x_1,x_2)·...·\sum_{x_n}P(x_1,x_2,...,x_n)$$

Is that correct?

By the way, I'm trying to calculate the joint probability.

You can find the book I'm using here, page 15.