= Positive-kernel comparison of thin-disk fields
{title2=$|\Sigma_M|<\Sigma\ \Longrightarrow\ |\partial_z\Phi_M|<\partial_z\Phi\quad(z>0)$}
The vertical field of a disk has kernel $Gz/(|\mathbf R-\mathbf R'|^2+z^2)^{3/2}>0$. The <triangle inequality> therefore bounds a signed-<surface density> field by the field of its absolute <surface density>. If that <surface density> is everywhere smaller than a nonnegative comparison <surface density>, their vertical fields satisfy the displayed strict comparison, provided the integrals exist and the strict bound holds on positive measure. This is useful when comparing <gravity-equivalent magnetic surface density> with actual disk mass.
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