= Interval discrepancy
{title2=$D_N(I)=\sum_{j=1}^N\mathbf1_I(u_j)-N|I|$}
Interval discrepancy measures the difference between empirical counts and the expected count for normalized <Lebesgue measure>. Convolving an enlarged interval <indicator function> with a narrow unit-integral <indicator function> gives a continuous majorant. Its <Fourier coefficients> decay as $O(1/(\delta k^2))$, converting the count into a constant term, finite exponential sums and a controlled absolute tail.
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