## §5.4: Degree-1 weight

In this section we prove two theorems about the degree-$1$ Fourier weight of boolean functions: $\mathbf{W}^{1}[f] = \sum_{i=1}^n \widehat{f}(i)^2.$

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## §2.3: Total influence

A very important quantity in the analysis of a boolean function is the sum of its influences.

Definition 26 The total influence of $f : \{-1,1\}^n \to {\mathbb R}$ is defined to be $\mathbf{I}[f] = \sum_{i=1}^n \mathbf{Inf}_i[f].$

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