Editing Benford's law (section)

===Benford’s law compliance theorem===
Mathematically, Benford’s law applies if the distribution being tested fits the "Benford’s law compliance theorem".<ref name="dspguide"/> The derivation says that Benford's law is followed if the [[Fourier transform]] of the logarithm of the probability density function is zero for all integer values. Most notably, this is satisfied if the Fourier transform is zero (or negligible) for ''n''&nbsp;≥&nbsp;1. This is satisfied if the distribution is wide (since wide distribution implies a narrow Fourier transform). Smith summarizes thus (p.&nbsp;716): 
<blockquote>
Benford's law is followed by distributions that are wide compared with unit distance along the logarithmic scale. Likewise, the law is not followed by distributions that are narrow compared with unit distance&nbsp;… If the distribution is wide compared with unit distance on the log axis, it means that the spread in the set of numbers being examined is much greater than ten.
</blockquote>

In short, Benford’s law requires that the numbers in the distribution being measured have a spread across at least an order of magnitude.