Fubini's theorem for finite series

Let

X

and

Y

be finite sets, and let

f : X \times Y \to R

be a function. Then

\begin{aligned} \sum_{x \in X} (\sum_{y \in Y} f (x, y)) & = [. . .] \\ = [. . .] \\ = [. . .] \end{aligned}

17.11.2019