= Balanced indicator function of a finite subset
{title2=$1_A-\alpha1_I$}
= Balanced subset indicator
{synonym}
For nonempty <finite set> $I$ and $A\subseteq I$, let $\alpha=|A|/|I|$ be the <density of a finite subset>. The balanced <indicator function> $f=1_A-\alpha1_I$, extended by zero to an ambient finite <group>, has sum zero and vanishing zero <Fourier coefficient>. The sum of $f$ on a subset $P\subseteq I$ is $|A\cap P|-\alpha|P|$, measuring the excess <density of a finite subset> there.
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