= Recovery of a loop measure from conformal deficits
{title2=$A(U)=\nu(\mathbf L_D\setminus\mathbf L_U)$}
For simple loops surrounding a marked point, containment in two simply connected domains is containment in their intersection component containing that point. Finite deficits therefore determine all finite intersections of avoidance events by <inclusion-exclusion>. Restrict to finite windows $H_r=\mathbf L_D\setminus\mathbf L_{rD}$ and use the <sigma-finite uniqueness theorem for measures>; as $r\downarrow0$ these windows exhaust the pointed loop space. Finiteness of the windows is essential to this argument.
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