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Math and science::Analysis::Tao::07. Series

Fubini's theorem for finite series

Let \( X \) and \( Y \) be finite sets, and let \( f: X \times Y \rightarrow R \) be a function. Then
\[ \begin{aligned}\sum_{x \in X}\left( \sum_{y \in Y}f(x,y) \right) &= [...] \\&= [...] \\&= [...]\end{aligned} \]