= Localized uncentered maximal weak-type inequality
{title2=$|E_\alpha|\leq3^d\nu(E_\alpha)/\alpha$}
For a positive <Borel measure> on $\mathbb R^d$, let $E_\alpha=\{M_u\nu>\alpha\}$, using open balls in the <uncentered maximal function of a finite measure>. Every ball witnessing the inequality lies entirely in $E_\alpha$. Cover a compact subset by finitely many witnessing balls and select disjoint balls greedily by decreasing radius. Their threefold dilations cover the compact set. Their total measure is at most $\nu(E_\alpha)$, giving the bound by <inner regularity of Lebesgue measure>. For a signed or complex measure, apply this to its <total variation measure>.
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